Chapter 6: Q 49E (page 572)

Factor by Grouping
In the following exercises, factor by grouping.
$2 x^{2} - 14 x - 5 x + 35$

Short Answer

Expert verified

The obtained factors for the expression $2 x^{2} - 14 x - 5 x + 35$ by using the grouping method are $(x - 7) (2 x - 5)$ .

Step by step solution

Given expression is,

$2 x^{2} - 14 x - 5 x + 35$ .

The objective is, we need to find the factors for this expression by using the grouping method.

First group the terms with the common factors.

$2 x^{2} - 14 x - 5 x + 35 = (2 x^{2} - 14 x) + (- 5 x + 35)$

Next factor out the common factors.

$2 x^{2} - 14 x - 5 x + 35 = 2 x (x - 7) - 5 (x - 7) = (x - 7) (2 x - 5)$

The obtained factors are, $(x - 7) (2 x - 5)$ .

Step 3 Let us check the answer by multiplying the factors.

$(x - 7) (2 x - 5) = 2 x^{2} - 5 x - 14 x + 35 = 2 x^{2} - 14 x - 5 x + 35$

which is true.

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Factor by Grouping
In the following exercises, factor by grouping.
$2 x^{2} - 14 x - 5 x + 35$

Short Answer

Step by step solution

Given expression is,

First group the terms with the common factors.

Step 3 Let us check the answer by multiplying the factors.

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Factor by GroupingIn the following exercises, factor by grouping.2x2−14x−5x+35

Short Answer

Step by step solution

Given expression is,

First group the terms with the common factors.

Step 3 Let us check the answer by multiplying the factors.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Calculus

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Factor by Grouping
In the following exercises, factor by grouping.
$2 x^{2} - 14 x - 5 x + 35$