Chapter 6: Q 67E (page 589)

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$x^{2} - 8 x + 12$

Short Answer

Expert verified

The factorization is $(x - 2) (x - 6)$ .

Step by step solution

Step 1. Writing the expression

Write the factors as two binomials with first terms $x$ .

localid="1644543979387" $(x) (x)$ .

Step 2. Finding the factors

We need to find two numbers whose product is $12$ and sum is $- 8$ .

Factors of $12$	Sum
$- 1, - 12$	$- 13$
$- 2, - 6$	$- 8$
$- 3, - 4$	$- 7$

Thus, $- 2$ and $- 6$ are the correct factors.

Hence, the factorization is $(x - 2) (x - 6)$ .

Step 3. Check

Multiply the factorization to get the trinomial again.

$(x - 2) (x - 6) = x^{2} - 6 x - 2 x + 12 (x - 2) (x - 6) = x^{2} - 8 x + 12$

Thus, the obtained factorization is correct.

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In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$x^{2} - 8 x + 12$

Short Answer

Step by step solution

Step 1. Writing the expression

Step 2. Finding the factors

Step 3. Check

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In the following exercises, factor each trinomial of the form x2+bx+c.x2-8x+12

Short Answer

Step by step solution

Step 1. Writing the expression

Step 2. Finding the factors

Step 3. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Calculus

Decision Maths

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$x^{2} - 8 x + 12$