Explanation Procedure used: Synthetic Division: Divide the polynomial by x − c : 1. Arrange the polynomial in descending powers, write 0 as coefficient of missing terms in the dividend. 2. Write c for the divisor x − c . 3. Bring down the leading coefficient of the dividend on the bottom row. 4. Multiply c times the value just written on the bottom row. Write the product in the next column in the second row. 5. Add the values in this new column, writing the sum in the bottom row and so on. 6. Use the numbers in the last row to write the quotient. The degree of the quotient is one less than the degree of the dividend. The last number in this row is the remainder”. Result used: If a is the zero of a polynomial function f ( x ) , then f ( a ) = 0 . Calculation: Consider the polynomial function g ( x ) = x 4 − 6 x 3 + x 2 + 24 x − 20 . Check whether the value of g ( 2 ) is 0 or not, in order to check that the number 2 is a zero of the polynomial function or not. 2 1 − 6 1 24 − 20 2 − 8 − 14 20 _ 1 − 4 − 7 10 0 From the above synthetic division, g ( 2 ) = 0

6th Edition

ISBN: 9780136175612

Author: BITTINGER

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4.3, Problem 34E

To determine

Whether the numbers 2 and –1 are zeros of the polynomial function g(x)=x4−6x3+x2+24x−20 by using synthetic division.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.3, Problem 33E

Chapter 4.3, Problem 35E

Students have asked these similar questions

The function f(x) is shown in the graph. 2 1 y -1 0 1 2 3 4 5 -1- -3. f(x) -4 -5 -6. Which type of function describes f(x)? ○ Exponential O Logarithmic ○ Rational O Polynomial .co. 6 7

The functions f(x) = –4x + 5 and g(x) = x3 + x2 – 4x + 5 are given.Part A: What type of functions are f(x) and g(x)? Justify your answer.Part B: Find the domain and range for f(x) and g(x). Then compare the domains and compare the ranges of the functions.

a) IS AU B is independence linear Show that A and B also independence linear or hot and why, write. Example. 6) 18 M., M2 X and dim(x)=n and dim M, dim M₂7 Show that Mi M₂+ {0} and why? c) let M Me X and {X.,... xr} is beas of M, and {y,, ., un} is beas of M₂ and {x, xr, Menyuzis beas of X Show that X = M₁ M2 d) 15 M₁ = {(x, y, z, w) | x+y=0, Z=2W} CR" M₂ = (X, Y, Z, W)/x+Y+Z=0}

Chapter 4 Solutions

COLLEGE ALGEBRA W/ ACCESS

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Whether the numbers 2 and –1 are zeros of the polynomial function g ( x ) = x 4 − 6 x 3 + x 2 + 24 x − 20 by using synthetic division.

Solution Summary: The author calculates whether the numbers 2 and –1 are zeros of the polynomial function g(x) by using synthetic division.

Videos

Whether the numbers 2 and –1 are zeros of the polynomial function g(x)=x4−6x3+x2+24x−20 by using synthetic division.

Want to see the full answer?

Chapter 4 Solutions