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Chapter 4: Q. 15 (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)=3x6+82x3+27;x+3

Short Answer

Expert verified

The remainder is0andx+3is a factor.

Step by step solution

01

Step 1. Given information.

The given function is,

f(x)=3x6+82x3+27;x+3

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+3, then the remainder is f(-3)that is

f(-3)=3-36+82-33+27=3729+82-27+27=2187-2214+27=-27+27=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=-3, then

f(c)=f(-3)=0

We observe that f(-3)=0,then x+3is a factor.

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