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Chapter 5: Q. 5.90 (page 549)

Use the Remainder Theorem to find the remainder when f(x)=x3鈭�7x+12 is divided by x+3.

Short Answer

Expert verified

The remainder is 6 whenf(x)=x3鈭�7x+12is divided byx+3.

Step by step solution

01

Step 1. Given Information

We want to find the remainder whenx3-7x+12is divided byx+3

We know that To use the Remainder Theorem, we must use the divisor in the x 鈭� c form.

We can write the divisor x+3asx鈭�(鈭�3).

So, our c is 鈭�3.

To find the remainder, we evaluate f (c) which is f (鈭�3).

02

Step 2. Evaluate f (−3)

To evaluate f (鈭�3), substitute x = 鈭�3 and simplify.

f(x)=x3鈭�7x+12f(-3)=(-3)3鈭�7(-3)+12f(-3)=-27+21+12f(-3)=6

The remainder is 6 when f(x)=x3鈭�7x+12is divided bylocalid="1646127157565" x+3.

03

Step 3. Check:

Use synthetic division to check.

The remainder is 6.

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