11/27/2021

Lesson 5 Homework Practice Factoring Linear Expressions

1. Attachments: Expressions Review Sheet.pdf Lesson-4Classwork.pdf Lesson-4Homework.pdf M3 L5 Factoring Linear Expressions Problem Solving Practice.pdf M3 Lesson 3 Adding Linear Expressions Day2 NY READY CC0001.pdf M3 Lesson 7 Homework.pdf.
2. \$16:(5 cannot be factored 32 + 24 x \$16:(5 8(4 + 3 x) 18 x + 6 \$16:(5 6(3 x + 1) The area of rectangle is (4 x ± 8) square units. Factor 4x ± 8 to find possible dimensions of the rectangle. \$16:(5 4 units by ( x ± 2) units Add or subtract. \$16:(5 x ± 2 \$16:(5 ±5 eSolutions Manual - Powered by Cognero Page 1 7-5 Factoring Linear Expressions.

The following steps will be useful to factor linear expressions.

Factoring Linear Expressions. In this math lesson, students learn how to factor linear expressions with rational coefficients by using the distributive property. The lesson helps students understand complex math concepts in an accessible way. This lesson is suitable for 7th grade students. Step 1 :

Find the largest common divisor for all the terms in the expression

Step 2 :

Divide each term of the expression by the largest common divisor.

Step 3:

Write the quotients inside the parenthesis.

Step 4 :

Write the largest common divisor and the parenthesis together using multiplication.

Examples

Example 1 :

Factor : 4x + 8

Solution :

Step 1 :

Find the largest common divisors for 4x and 8.

The largest common divisor for 4x and 8 is 4.

Step 2 :

Divide 4x and 8 by 4

4x / 4 = x and 8 / 4 = 2

Step 3 :

Write the quotients x and 2 inside the parenthesis and multiply by the largest common divisor 4.

4(x + 2)

Example 2 :

Factor : 16a + 64b - 4c

Solution :

Step 1 :

Find the largest common divisors for 16a, 64b and 4c.

The largest common divisor for 16a, 64b and 4c is 4.

Step 2 :

Divide 16a, 64b and 4c by 4

16a / 4 = 4a, 64b / 4 = 16b and 4c / 4 = c

Step 3 :

Write the quotients 4a, 16b and c inside the parenthesis and multiply by the largest common divisor 4.

4(4a + 16b - c)

Example 3 :

Factor : 36x - 16

Solution :

Step 1 :

Find the largest common divisors for 36x and 16.

The largest common divisor for 36x and 16 is 4.

Step 2 :

Divide 36x and - 16 by 4.

36x / 4 = 9x and -16 / 4 = -4

Step 3 :

Write the quotients 9x and -4 inside the parenthesis and multiply by the largest common divisor 4.

4(9x - 4)

Example 4 :

Factor : 35 + 21 a

Solution :

Step 1 :

Find the largest common divisors for 35 and 21a.

The largest common divisor for 35 and 21a is 7.

Step 2 :

Divide each term by 7

35 / 7 = 5, 21a/ 7 = 3a

Step 3 :

Write the quotients 5 and 3a inside the parenthesis and multiply by the largest common divisor 7.

7 (5 + 3a)

Example 5 :

Factor : 4a - 8b + 5ax - 10bx

Solution :

Step 1 :

Factoring Linear Expressions Examples

Since we have four terms, we can group them into two terms

= 4a - 8b + 5ax - 10bx

Common divisor for first two terms, that is 4a and 8b is 4

Common divisor for third and fourth terms, that is 5ax and 10bx is 5x.

Step 2 :

Divide first two terms by 4

4a/4 = 1a

- 8b/4 = -2b

Divide third and fourth terms by 5x

5ax/5x = a

- 10bx/5x = -2b

Step 3 :

= 4(a - 2b) + 5x (a - 2b)

= (a - 2b) (4 + 5x)

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