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ax"is the leading term, a is the leading coefficient, and a, is the constant term. The terms of a polynomial may be written in any order. However, if they are written in decreasing powers of, we say that the polynomial function is in standard form. Illustrative Example. A polynomial function f(x) = 4x° + 2x° + x + 6 can be written in standard form as f(x) = 2x'+ 4x + x+6. It is of degree 3; its leading term is 2x' ; its leading coefficient is 2; and its constant term is 6. Activity 1: Fix and Move Them, then Fill Me UP Consider the given polynomial functions and fill in the table below. Polynomial Function Polynomial function in standard position Leading Coefficient Constant Term Degree 1. f(x) = 3x²- 2x' + x- 3 |2.f(x) = 3 + 3x'- 2x + x² 3. f(x) = 6x²- 2x + x – 3 4. f(x) = 1 + x-5x

ax"is the leading term, a is the leading coefficient, and a, is the constant term. The terms of a polynomial may be written in any order. However, if they are written in decreasing powers of, we say that the polynomial function is in standard form. Illustrative Example. A polynomial function f(x) = 4x° + 2x° + x + 6 can be written in standard form as f(x) = 2x'+ 4x + x+6. It is of degree 3; its leading term is 2x' ; its leading coefficient is 2; and its constant term is 6. Activity 1: Fix and Move Them, then Fill Me UP Consider the given polynomial functions and fill in the table below. Polynomial Function Polynomial function in standard position Leading Coefficient Constant Term Degree 1. f(x) = 3x²- 2x' + x- 3 |2.f(x) = 3 + 3x'- 2x + x² 3. f(x) = 6x²- 2x + x – 3 4. f(x) = 1 + x-5x

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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ull Globe ? 12:55 AM 1 @ 59% Week 1 LAS 1_.. МАТНЕMАТICS 10 Quarter 2 Name: Date: Year and Section: Parent/Guardian's Signature: Week 1 LAS1: Illustrates Polynomial Functions A polynomial function is a function of the form P(x) = a_x + . + a,x + a, a̟#0, n is a nonnegative integer, a,a, ..., a are all real numbers called coefficients, where a x" is the leading term, a_is the leading coefficient, and a is the constant term. The terms of a polynomial may be written in any order. However, if they are written in decreasing powers of, we say that the polynomial function is in standard form. Illustrative Example. A polynomial function f(x) = 4x + 2x + x+6 can be written in standard form as f(x) = 2x'+ 4x + x + 6. It is of degree 3; its leading term is 2x' ; its leading coefficient is 2; and its constant term is 6. Activity 1: Fix and Move Them, then Fill Me UP Consider the given polynomial functions and fill in the table below. Polynomial Function Polynomial function in standard position Degree Leading Coefficient Constant Term |1. f(x) = 3x- 2x' +x- 3 2.f(x) = 3 + 3x. 2x + x 3. f(x) = 6x- 2x + x - 3 4. f(x) = 1+ x-5x
Transcribed Image Text:ull Globe ? 12:55 AM 1 @ 59% Week 1 LAS 1_.. МАТНЕMАТICS 10 Quarter 2 Name: Date: Year and Section: Parent/Guardian's Signature: Week 1 LAS1: Illustrates Polynomial Functions A polynomial function is a function of the form P(x) = a_x + . + a,x + a, a̟#0, n is a nonnegative integer, a,a, ..., a are all real numbers called coefficients, where a x" is the leading term, a_is the leading coefficient, and a is the constant term. The terms of a polynomial may be written in any order. However, if they are written in decreasing powers of, we say that the polynomial function is in standard form. Illustrative Example. A polynomial function f(x) = 4x + 2x + x+6 can be written in standard form as f(x) = 2x'+ 4x + x + 6. It is of degree 3; its leading term is 2x' ; its leading coefficient is 2; and its constant term is 6. Activity 1: Fix and Move Them, then Fill Me UP Consider the given polynomial functions and fill in the table below. Polynomial Function Polynomial function in standard position Degree Leading Coefficient Constant Term |1. f(x) = 3x- 2x' +x- 3 2.f(x) = 3 + 3x. 2x + x 3. f(x) = 6x- 2x + x - 3 4. f(x) = 1+ x-5x
ll Globe ? 12:55 AM 1 © 60% Week 1 LAS 2... MATHEMATICS 10 Quarter 2 Name: Date: Year and Section: Parent/Guardian's Signature: Week 1 LAS 2: Illustrates Polynomial Functions Polynomials may also be written in factored form and as a product of irreducible factors, that is, a factor that can no longer be factored using coefficients that are real numbers. Here are some examples. a. y = x-5x - 24 in factored form is y = (x- 8) (x + 3) b. y = -x + 9x in factored form is y = x(x + 3)(x - 3) c. y = 2x + 5x + 7x- 5 in factored form is y =( x + 3x + 5)(2x - 1) d. f(x) = x + x + 18 in factored form is f(x) = (x²- 2x + 6)(x + 3) e. f(x) = x +x - 12x in factored form is f(x) = x(x + 4)(x - 3) Activity 2: Do You Miss Me? Here I am Again Write the following polynomial functions in factored form. 1. f(x) = 2x -11x + 5 2. f(x) = x - 5x 3. f(x) = (2x - 5x + 3) (x - 3) 4. f(x) = x+ 5x + 6 5. f(x) = (x - 1) (x² - 5x + 6)
Transcribed Image Text:ll Globe ? 12:55 AM 1 © 60% Week 1 LAS 2... MATHEMATICS 10 Quarter 2 Name: Date: Year and Section: Parent/Guardian's Signature: Week 1 LAS 2: Illustrates Polynomial Functions Polynomials may also be written in factored form and as a product of irreducible factors, that is, a factor that can no longer be factored using coefficients that are real numbers. Here are some examples. a. y = x-5x - 24 in factored form is y = (x- 8) (x + 3) b. y = -x + 9x in factored form is y = x(x + 3)(x - 3) c. y = 2x + 5x + 7x- 5 in factored form is y =( x + 3x + 5)(2x - 1) d. f(x) = x + x + 18 in factored form is f(x) = (x²- 2x + 6)(x + 3) e. f(x) = x +x - 12x in factored form is f(x) = x(x + 4)(x - 3) Activity 2: Do You Miss Me? Here I am Again Write the following polynomial functions in factored form. 1. f(x) = 2x -11x + 5 2. f(x) = x - 5x 3. f(x) = (2x - 5x + 3) (x - 3) 4. f(x) = x+ 5x + 6 5. f(x) = (x - 1) (x² - 5x + 6)
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