Chapter 8: Q20. (page 492)

Factor each polynomial.
$x^{2} - 4 x - 21$

Short Answer

Expert verified

The factors of the given polynomial are $(x + 3) (x - 7)$ .

Step by step solution

Step 1. Compare.

Compare a given trinomial to $a x^{2} + b x + c$ and write the values of $a, b$ and role="math" localid="1647519883705" $c$ .

$a = 1 b = - 4 c = - 21$

Step 2. List the factors.

List the factors of $- 21$ , where one factor of each pair is negative. Look for the pair of factors with a sum of $- 4$ .

Factors of $- 21$	Sum of factors
$1, - 21$	$- 20$
$3, - 7$	$- 4$

Therefore, the correct factors are 3 and $- 7$ .

Step 3. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of $- 21$ and sum of $- 4$ . The numbers are 3 and $- 7$ .

role="math" localid="1647520367081" $x^{2} - 4 x - 21 = (x + m) (x + p) = (x + 3) (x - 7)$

Therefore, the factors of $x^{2} - 4 x - 21$ are $(x + 3) (x - 7)$ .

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Factor each polynomial.
$x^{2} - 4 x - 21$

Short Answer

Step by step solution

Step 1. Compare.

Step 2. List the factors.

Step 3. Apply factoring pattern of ax2+bx+c.

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Factor each polynomial.x2-4x-21

Short Answer

Step by step solution

Step 1. Compare.

Step 2. List the factors.

Step 3. Apply factoring pattern of ax2+bx+c.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Geometry

Decision Maths

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Factor each polynomial.
$x^{2} - 4 x - 21$