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Chapter 4: Q. 14 (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).

f(x)=4x4-15x2-4;x-2

Short Answer

Expert verified

The remainder is 0and x-2is a factor.

Step by step solution

01

Step 1. GIven information.

The given function is,

f(x)=4x4-15x2-4;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)=424-1522-4=416-154-4=64-60-4=0

Therefore, the remainder is 0.

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)=0

We observe that f(2)=0,then x-2is a factor.

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