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Chapter 4: Q. 11 (page 209)

Use the Remainder Theorem to find the remainder when f(x)is divided by x-c. Then use the Factor Theorem to determine whether x-cis a factor of f(x).

role="math" localid="1646221007063" f(x)=4x3-3x2-8x+4;x-2

Short Answer

Expert verified

The remainder is 8and x-2is not a factor.

Step by step solution

01

Step 1. Given information.

The given function is,

f(x)=4x3-3x2-8x+4;x-2

02

Step 2. Using remainder theorem.

We know that if f(x)is divided by x-cthen the remainder will be f(c).

Here f(x)is divided by x-2, then the remainder is f(2)that is

f(2)=423-322-82+4=48-34-16+4=32-12-12=32-24=8

Therefore, the remainder is8.

03

Step 3. Using factor theorem.

We know that if x-cis the factor of the polynomial f(x)then

f(c)=0,

Here c=2, then

f(c)=f(2)=8

We observe that f(2)鈮�0,then x-2is not a factor.

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