Factor Expressions 1

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Pre - Algebra

Factoring

Factor Expressions

Factor Expressions 1

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Question 1 of 5

1. Question
Factor.

$4 m - 28$ $4m-28$
- 1. $5 (2 m - 14)$ $5(2m-14)$
- 2. $4 (m + 11)$ $4(m+11)$
- 3. $5 (m + 3)$ $5(m+3)$
- 4. $4 (m - 7)$ $4(m-7)$
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A Greatest Common Factor is the factor of two terms with the highest value.

First, find the Greatest Common Factor (GCF) of the two terms.

Factors of $4 m$ $4m$ : $4$ $4$ $\times m$ $times m$

Factors of $28$ $28$ : $4$ $4$ $\times 7$ $times7$

Both terms have $4$ $4$ as their factor, so it is the GCF.

Finally, factor by placing $4$ $4$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $4$ $4$ , then simplify.

$4 [(4 m \div 4) - (28 \div 4)]$ $4[(4mdiv4)-(28div4)]$

$=$ $=$ $4 (m - 7)$ $4(m-7)$

$4 (m - 7)$ $4(m-7)$
Question 2 of 5

2. Question
Factor.

$5 x - 35 y$ $5x-35y$
- 1. $5 (x - 7 y)$ $5(x-7y)$
- 2. $5 (2 x - 5 y)$ $5(2x-5y)$
- 3. $7 (2 x - 3 y)$ $7(2x-3y)$
- 4. $5 (3 x - 4 y)$ $5(3x-4y)$
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A Greatest Common Factor is the factor of two terms with the highest value.

First, find the Greatest Common Factor (GCF) of the two terms.

Factors of $5 x$ $5x$ : $5$ $5$ $\times x$ $times x$

Factors of $35 y$ $35y$ : $5$ $5$ $\times 7 \times y$ $times7timesy$

Both terms have $5$ $5$ as their factor, so it is the GCF.

Finally, factor by placing $5$ $5$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $5$ $5$ , then simplify.

$5 [(5 x \div 5) - (35 y \div 5)]$ $5[(5xdiv5)-(35ydiv5)]$

$=$ $=$ $5(x-7y)$

$5(x-7y)$
Question 3 of 5

3. Question
Factor.

$a^2+5a$
- 1. $a(a+5)$
- 2. $5(a^2+a)$
- 3. $a(5a+5)$
- 4. $a(a^2+5)$
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A Greatest Common Factor is the factor of two terms with the highest value.

First, find the Greatest Common Factor (GCF) of the two terms.

Factors of $a^2$ : $a$ $times a$

Factors of $5a$ : $5times$ $a$

Both terms have $a$ as their factor, so it is the GCF.

Finally, factor by placing $a$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $a$ , then simplify.

$a[(a^2diva)+(5adiva)]$

$=$ $a(a+5)$

$a(a+5)$
Question 4 of 5

4. Question
Factor.

$35x+42$
- 1. $14(3x+4)$
- 2. $7(28x+35)$
- 3. $7(5x+6)$
- 4. $5(7x+12)$
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A Greatest Common Factor is the factor of two terms with the highest value.

First, find the Greatest Common Factor (GCF) of the two terms.

Factors of $35x$ : $5times$ $7$ $times x$

Factors of $42$ : $7$ $times6$

Both terms have $7$ as their factor, so it is the GCF.

Finally, factor by placing $7$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $7$ , then simplify.

$7[(35xdiv7)+(42div7)]$

$=$ $7(5x+6)$

$7(5x+6)$
Question 5 of 5

5. Question
Factor.

$40+72a$
- 1. $5(5+7a)$
- 2. $3(9+16a)$
- 3. $8(5+9a)$
- 4. $6(6+12a)$
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A Greatest Common Factor is the factor of two terms with the highest value.

First, find the Greatest Common Factor (GCF) of the two terms.

Factors of $40$ : $8$ $times5$

Factors of $72a$ : $8$ $times9timesa$

Both terms have $8$ as their factor, so it is the GCF.

Finally, factor by placing $8$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $8$ , then simplify.

$8[(40div8)+(72adiv8)]$

$=$ $8(5+9a)$

$8(5+9a)$

Factor Expressions 1

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Quiz summary

Information

1. Question

Hint

Keep Going!

2. Question

Hint

Correct!

3. Question

Hint

Fantastic!

4. Question

Hint

Great Work!

5. Question

Hint

Excellent!

Quizzes

		$4 [(4 m \div 4) - (28 \div 4)]$ $4[(4mdiv4)-(28div4)]$
	$=$ $=$	$4 (m - 7)$ $4(m-7)$

		$5 [(5 x \div 5) - (35 y \div 5)]$ $5[(5xdiv5)-(35ydiv5)]$
	$=$ $=$	$5(x-7y)$

		$a[(a^2diva)+(5adiva)]$
	$=$	$a(a+5)$

		$7[(35xdiv7)+(42div7)]$
	$=$	$7(5x+6)$

		$8[(40div8)+(72adiv8)]$
	$=$	$8(5+9a)$