Chapter 7: Q. 379 (page 898)

Factor Trinomials of the form $x^{2} + b x + c$
$k^{2} - 16 k + 60$

Short Answer

Expert verified

Factor is: $k^{2} - 16 k + 60 = (k - 10) (k - 6)$

Step by step solution

Step 1. Given information

given expression $k^{2} - 16 k + 60$

Step 2. Factor the expression by grouping.

First, the expression needs to be rewritten as $k^{2} + a k + b k + 60$ . To find $a$ and $b$ , set up a system to be solved.

$a + b = - 16 a b = 60$

Step 3. Find a and b

by guessing all such integer pairs that give the product $60$

we find

$a = - 10, b = - 6$

Rewrite the expression $k^{2} - 16 k + 60$ as $k^{2} - 10 k - 6 k + 60$

Step 4. Now factor by grouping

$k^{2} - 10 k - 6 k + 60 = (k^{2} - 10 k) (- 6 k + 60) = k (k - 10) - 6 (k - 10) = (k - 10) (k - 6)$

Therefore, the factor of the given expression is $(k - 10) (k - 6)$

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Factor Trinomials of the form $x^{2} + b x + c$
$k^{2} - 16 k + 60$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factor the expression by grouping.

Step 3. Find a and b

Step 4. Now factor by grouping

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Factor Trinomials of the form x2+bx+ck2−16k+60

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factor the expression by grouping.

Step 3. Find a and b

Step 4. Now factor by grouping

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Factor Trinomials of the form $x^{2} + b x + c$
$k^{2} - 16 k + 60$