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Chapter 4: Q. 19 (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)=2x4-x3+2x-1;x-12

Short Answer

Expert verified

The remainder is 0and x-12is a factor.

Step by step solution

01

Step 1. Given information.

The given function is,

f(x)=2x4-x3+2x-1;x-12.

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-12, then the remainder is f12that is

f12=2124-123+212-1=2116-18+1-1=18-18=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=12, then

f(c)=f12=0

We observe that f12=0,then x-12is a factor.

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