Elementary Technical Mathematics
12th Edition
ISBN: 9781337630580
Author: Dale Ewen
Publisher: Cengage Learning
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Chapter 5.5, Problem 4E
To determine
To calculate: The product of the expression
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An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
Steel Production Planning:
Let S represent the amount of steel produced (in tons). Steel Production is related to the amount of labor used(L) and the amount of capital used ( C ) by the following function:S = 20L⁰˙³⁰C⁰˙⁷⁰In this formula L represents the units of Labor input and C the units of Capital input. Each unit of Labor costs $50, and each unit of Capital costs $100.
a:Formulate an optimization problem that will determine how much labor and capital are needed to produce 50,000 tons of steel at minimum cost.
Q#3B: Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L>0 and C>0.)…
Chapter 5 Solutions
Elementary Technical Mathematics
Ch. 5.1 - Prob. 1ECh. 5.1 - Evaluate each expression: (2)(3)2+3(2)6Ch. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Evaluate each expression: (9)233(6)+[ 3(2)5(3) ]Ch. 5.1 - Evaluate each expression: [ (2)(8)2(2)3 ][ 4+(2)4...Ch. 5.1 - Prob. 10E
Ch. 5.1 - In Exercise 11-16, let x=2 and y=3, and evaluate...Ch. 5.1 - In Exercise 11-16, let x=2 and y=3, and evaluate...Ch. 5.1 - In Exercise 11-16, let x=2 and y=3, and evaluate...Ch. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - In Exercise 11-16, let x=2 and y=3, and evaluate...Ch. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - Prob. 24ECh. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - In Exercise 17-26, let x=1 and y=5, and evaluate...Ch. 5.1 - In Exercises 27-32, let x=3,y=4,andz=6 . Evaluate...Ch. 5.1 - In Exercises 27-32, let x=3,y=4,andz=6 . Evaluate...Ch. 5.1 - In Exercises 27-32, let x=3,y=4,andz=6 . Evaluate...Ch. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - In Exercises 33-42, let x=1,y=2,andz=3 . Evaluate...Ch. 5.1 - Prob. 34ECh. 5.1 - In Exercises 33-42, let x=1,y=2,andz=3 . Evaluate...Ch. 5.1 - Prob. 36ECh. 5.1 - In Exercises 33-42, let x=1,y=2,andz=3 . Evaluate...Ch. 5.1 - In Exercises 33-42, let x=1,y=2,andz=3 . Evaluate...Ch. 5.1 - Prob. 39ECh. 5.1 - In Exercises 33-42, let x=1,y=2,andz=3 . Evaluate...Ch. 5.1 - In Exercises 33-42, let x=1,y=2,andz=3 . Evaluate...Ch. 5.1 - In Exercises 33-42, let x=1,y=2,andz=3 . Evaluate...Ch. 5.2 - Remove the parentheses from each expression:...Ch. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Remove the parentheses from each expression:...Ch. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Remove the parentheses from each expression:...Ch. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Remove the parentheses from each expression:...Ch. 5.2 - Remove the parentheses from each expression:...Ch. 5.2 - Remove the parentheses from each expression:...Ch. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Combine the like terms: 6a2+a+12aCh. 5.2 - Combine the like terms: 5x2+3x28x2Ch. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Combine the like terms: 3x25x2+4x2+x4+5x2x+2Ch. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Simplify by first removing the parentheses and...Ch. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Simplify by first removing the parentheses and...Ch. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - Simplify by first removing the parentheses and...Ch. 5.2 - Prob. 64ECh. 5.2 - Prob. 65ECh. 5.2 - Simplify by first removing the parentheses and...Ch. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Prob. 70ECh. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.2 - Simplify by first removing the parentheses and...Ch. 5.2 - Prob. 74ECh. 5.2 - Prob. 75ECh. 5.2 - Prob. 76ECh. 5.2 - Simplify by first removing the parentheses and...Ch. 5.2 - Prob. 78ECh. 5.3 - Classify each expression as a monomial, a...Ch. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Classify each expression as a monomial, a...Ch. 5.3 - Prob. 7ECh. 5.3 - Classify each expression as a monomial, a...Ch. 5.3 - Classify each expression as a monomial, a...Ch. 5.3 - Classify each expression as a monomial, a...Ch. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Rearrange each polynomial in decreasing order and...Ch. 5.3 - Rearrange each polynomial in decreasing order and...Ch. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Rearrange each polynomial in decreasing order and...Ch. 5.3 - Rearrange each polynomial in decreasing order and...Ch. 5.3 - Rearrange each polynomial in decreasing order and...Ch. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Add the following polynomials: (6x27x+5)+(3x2+2x5)Ch. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Find each difference: (3x25x+4)(6x27x+2)Ch. 5.3 - Find each difference: (13x2x2)(15x+x2)Ch. 5.3 - Find each difference: (3a4b)(2a7b)Ch. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Find each difference: (20w217w6)(13w2+7w)Ch. 5.3 - Find each difference: (y22y+1)(2y2+3y+5)Ch. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Subtract the following polynomials:...Ch. 5.3 - Subtract the following polynomials:...Ch. 5.3 - Prob. 58ECh. 5.4 - Find each product: (3a)(5)Ch. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Find each product: (9m2)(6m2)Ch. 5.4 - Prob. 6ECh. 5.4 - Find each product: (8a6)(4a2)Ch. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Find each product: (6n)(5n2m)Ch. 5.4 - Find each product: (9ab2)(6a2b3)Ch. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Find each product: (8a2bc)(3ab3c2)Ch. 5.4 - Find each product: (4xy2z3)(4x5z3)Ch. 5.4 - Find each product: (23x2y)(932xy4z3)Ch. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Use the rules for exponents to simplify: (xy)4Ch. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Use the rules for exponents to simplify: (3x4)2Ch. 5.4 - Use the rules for exponents to simplify: (5x2)3Ch. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Use the rules for exponents to simplify: (x2x3)2Ch. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Use the rules for exponents to simplify: (5x3y2)2Ch. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Use the rules for exponents to simplify: (16x4x5)3Ch. 5.4 - Use the rules for exponents to simplify: (2x3y4z)3Ch. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Evaluate each expression when a=2andb=3: b4Ch. 5.5 - Find each product. 4(a+6)Ch. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Find each product. 3x(4x27x2)Ch. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Find each product. 6x3(16x2+9x4)Ch. 5.5 - Find each product. 5x4(2x3+8x21)Ch. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Find each product. (x+1)(x+6)Ch. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41ECh. 5.5 - Prob. 42ECh. 5.5 - Prob. 43ECh. 5.5 - Prob. 44ECh. 5.5 - Find each product. (6a+4)(2a3)Ch. 5.5 - Prob. 46ECh. 5.5 - Prob. 47ECh. 5.5 - Prob. 48ECh. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - Prob. 51ECh. 5.5 - Prob. 52ECh. 5.5 - Prob. 53ECh. 5.5 - Prob. 54ECh. 5.5 - Prob. 55ECh. 5.5 - Prob. 56ECh. 5.5 - Prob. 57ECh. 5.5 - Prob. 58ECh. 5.5 - Prob. 59ECh. 5.5 - Prob. 60ECh. 5.5 - Prob. 61ECh. 5.5 - Prob. 62ECh. 5.5 - Find each product. (g+h6)(gh+3)Ch. 5.5 - Find each product. (2x3y+4)(4x5y2)Ch. 5.5 - Find each product. (8xx3+2x41)(x2+2+5x3)Ch. 5.5 - Prob. 66ECh. 5.6 - Divide: 9x53x3Ch. 5.6 - Prob. 2ECh. 5.6 - Divide: 18x1212x4Ch. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Divide: 8x212xCh. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Prob. 15ECh. 5.6 - Prob. 16ECh. 5.6 - Divide: 0(113w2r3)Ch. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Divide: (42x2y3)(14x2y4)Ch. 5.6 - Prob. 21ECh. 5.6 - Prob. 22ECh. 5.6 - Prob. 23ECh. 5.6 - Prob. 24ECh. 5.6 - Divide: 92x3y28xy3Ch. 5.6 - Prob. 26ECh. 5.6 - Prob. 27ECh. 5.6 - Prob. 28ECh. 5.6 - Prob. 29ECh. 5.6 - Prob. 30ECh. 5.6 - Prob. 31ECh. 5.6 - Prob. 32ECh. 5.6 - Prob. 33ECh. 5.6 - Prob. 34ECh. 5.6 - Prob. 35ECh. 5.6 - Prob. 36ECh. 5.6 - Divide: 24a416a28a8Ch. 5.6 - Prob. 38ECh. 5.6 - Prob. 39ECh. 5.6 - Prob. 40ECh. 5.6 - Divide: bx4bx3+bx24bxbxCh. 5.6 - Prob. 42ECh. 5.6 - Prob. 43ECh. 5.6 - Prob. 44ECh. 5.6 - Divide: 224x4y2z3168x3y2z4112xy4z228xy2z2Ch. 5.6 - Prob. 46ECh. 5.6 - Prob. 47ECh. 5.6 - Divide: 3a2b+4a2b26ab22ab2Ch. 5.6 - Prob. 49ECh. 5.6 - Divide: 18w4r4+27w3r336w2r29w3r3Ch. 5.7 - Find each quotient and check: (x2+3x+2)(x+1)Ch. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Prob. 6ECh. 5.7 - Find each quotient and check: 2y2+3y52y1Ch. 5.7 - Prob. 8ECh. 5.7 - Prob. 9ECh. 5.7 - Prob. 10ECh. 5.7 - Prob. 11ECh. 5.7 - Find each quotient and check: (8x318x2+7x+3)(x1)Ch. 5.7 - Find each quotient and check:...Ch. 5.7 - Prob. 14ECh. 5.7 - Find each quotient and check: 2x314x12x+1Ch. 5.7 - Prob. 16ECh. 5.7 - Prob. 17ECh. 5.7 - Prob. 18ECh. 5.7 - Prob. 19ECh. 5.7 - Find each quotient and check: 2x3+3x29x+5x+3Ch. 5.7 - Prob. 21ECh. 5.7 - Prob. 22ECh. 5.7 - Prob. 23ECh. 5.7 - Prob. 24ECh. 5.7 - Find each quotient and check: 8x312x+1Ch. 5.7 - Prob. 26ECh. 5.7 - Prob. 27ECh. 5.7 - Prob. 28ECh. 5.7 - Prob. 29ECh. 5.7 - Find each quotient and check:...Ch. 5 - Prob. 1RCh. 5 - Prob. 2RCh. 5 - For any number a expect 0, a,a1a=?Ch. 5 - Evaluate: 104(3)Ch. 5 - Evaluate: 2+342Ch. 5 - Evaluate: (4)(12)623+1832Ch. 5 - In Exercises 7-12, let x=3andy=2 . Evaluate each...Ch. 5 - In Exercises 7-12, let x=3andy=2 . Evaluate each...Ch. 5 - In Exercises 7-12, let x=3andy=2 . Evaluate each...Ch. 5 - In Exercises 7-12, let x=3andy=2 . Evaluate each...Ch. 5 - In Exercises 7-12, let x=3andy=2 . Evaluate each...Ch. 5 - In Exercises 7-12, let x=3andy=2 . Evaluate each...Ch. 5 - In Exercises 13-16, simplify by removing the...Ch. 5 - In Exercises 13-16, simplify by removing the...Ch. 5 - In Exercises 13-16, simplify by removing the...Ch. 5 - In Exercises 13-16, simplify by removing the...Ch. 5 - Prob. 17RCh. 5 - Prob. 18RCh. 5 - Perform the indicated operation:...Ch. 5 - Perform the indicated operation:...Ch. 5 - Perform the indicated operation:...Ch. 5 - Perform the indicated operation: (6x2)(4x3)Ch. 5 - Perform the indicated operation: (7x2y)(8x3y2)Ch. 5 - Prob. 24RCh. 5 - Perform the indicated operation: 5a(3a+4b)Ch. 5 - Prob. 26RCh. 5 - Perform the indicated operation: (5x+3)(3x4)Ch. 5 - Prob. 28RCh. 5 - Perform the indicated operation: (49x2)(7x3)Ch. 5 - Prob. 30RCh. 5 - Perform the indicated operation: 36a327a2+9a9aCh. 5 - Perform the indicated operation: 6x2+x122x+3Ch. 5 - Perform the indicated operation: 3x3+2x26x+4x+2Ch. 5 - Evaluate: 35242Ch. 5 - Evaluate: 12232+331622Ch. 5 - Evaluate each expression when x=4andy=1. 4x23y3Ch. 5 - Evaluate each expression when x=4andy=1. 2x2y4x2yCh. 5 - Is 4+3x5x2 a monomial, a binomial, or a trinomial?...Ch. 5 - Rearrange the polynomial 3+4x25x3x in decreasing...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify: Add:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...Ch. 5 - Perform the indicated operation and simplify:...
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ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Polynomials with Trigonometric Solutions (2 of 3: Substitute & solve); Author: Eddie Woo;https://www.youtube.com/watch?v=EnfhYp4o20w;License: Standard YouTube License, CC-BY
Quick Revision of Polynomials | Tricks to Solve Polynomials in Algebra | Maths Tricks | Letstute; Author: Let'stute;https://www.youtube.com/watch?v=YmDnGcol-gs;License: Standard YouTube License, CC-BY
Introduction to Polynomials; Author: Professor Dave Explains;https://www.youtube.com/watch?v=nPPNgin7W7Y;License: Standard Youtube License