(x – 5)(x+2) × the complete factorization of f(x) is x³ - 19x – 3 = %3D

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.3: Dividing Polynomials
Problem 2E: (a) If we divide the polynomial P(x) by the factor xc and we obtain a remainder of 0, then we know...
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X^3-19x-30=0. , X= -3
examining the remalnder.
-3 1
-19
-30
-3
6.
A30
1-3
-10
Step 2
The Factor Theorem states that a polynomial f(x) has a factor (x – k) if and only if f(k) = 0.
The remainder r obtained in the synthetic division is r = 0. So, f(-3)% = 0 and (x + 3)
is
a
factor.
Step 3
Here, the remainder is zero and the quotient is x - 3x – 10. So, by using the Division Algorithm, we can
write the result as
(2 - 3x - 10).
x3 - 19x- 30 = (x + 3)
Now factor the quadratic expression (x – 3x – 10).
(*2 - 3x - 10) -
Ja+2)
x- 5
%3D
Therefore, the complete factorization of f(x) is x - 19x – 30 = (x – 5) (x +2) x
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Transcribed Image Text:examining the remalnder. -3 1 -19 -30 -3 6. A30 1-3 -10 Step 2 The Factor Theorem states that a polynomial f(x) has a factor (x – k) if and only if f(k) = 0. The remainder r obtained in the synthetic division is r = 0. So, f(-3)% = 0 and (x + 3) is a factor. Step 3 Here, the remainder is zero and the quotient is x - 3x – 10. So, by using the Division Algorithm, we can write the result as (2 - 3x - 10). x3 - 19x- 30 = (x + 3) Now factor the quadratic expression (x – 3x – 10). (*2 - 3x - 10) - Ja+2) x- 5 %3D Therefore, the complete factorization of f(x) is x - 19x – 30 = (x – 5) (x +2) x Submit Skip (you cannot come back)
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