Chapter 5: Q. 5.90 (page 549)

Use the Remainder Theorem to find the remainder when $f (x) = x^{3} - 7 x + 12$ is divided by $x + 3$ .

Short Answer

Expert verified

The remainder is 6 when $f (x) = x^{3} - 7 x + 12$ is divided by $x + 3$ .

Step by step solution

Step 1. Given Information

We want to find the remainder when $x^{3} - 7 x + 12$ is divided by $x + 3$

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

We can write the divisor $x + 3$ as $x - (- 3) .$

So, our c is −3.

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

Step 2. Evaluate f (−3)

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

f (x) = x^{3} - 7 x + 12 f (- 3) = {(- 3)}^{3} - 7 (- 3) + 12 f (- 3) = - 27 + 21 + 12 f (- 3) = 6

The remainder is 6 when $f (x) = x^{3} - 7 x + 12$ is divided bylocalid="1646127157565" $x + 3$ .

Step 3. Check:

Use synthetic division to check.

The remainder is 6.

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Use the Remainder Theorem to find the remainder when $f (x) = x^{3} - 7 x + 12$ is divided by $x + 3$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Evaluate f (−3)

Step 3. Check:

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Evaluate f (−3)

Step 3. Check:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Use the Remainder Theorem to find the remainder when $f (x) = x^{3} - 7 x + 12$ is divided by $x + 3$ .