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Chapter 5: Q.335. (page 552)

Use the factor theorem to determine whetherx+4a factor ofrole="math" localid="1644481853619" x3+x2-14x+8.

Short Answer

Expert verified

No,x+4is not a factor ofx3+x2-14x+8.

Step by step solution

01

Step 1. Given information.

x3+x2-14x+8andx+4is the factor of polynomial function.

02

Step 2. To simplify the polynomial function, by using remainder theorem.

According to the remainder theorem x+4is a factor of f(x)=x3+x2-14x+8if role="math" localid="1644482118328" f-4=0.

Substitute x=-4in f(x)=x3+x2-14x+8.

f(-4)=-43+-42-14-4+8鈬�-64+16+56+8鈬�-64+80鈬�-16

03

Step 3. Simplified answer.

Sincef-4is not equal to zero, sox+4is not a factor off(x)=x3+x2-14x+8.

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