Factor Expressions 1

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Algebra 1

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. $7 (2 x - 3 y)$ $7(2x-3y)$
- 2. $5 (3 x - 4 y)$ $5(3x-4y)$
- 3. $5 (2 x - 5 y)$ $5(2x-5y)$
- 4. $5 (x - 7 y)$ $5(x-7y)$
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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.

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

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

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

3. Question
Factor.

$a^{2} + 5 a$ $a^2+5a$
- 1. $a (a^{2} + 5)$ $a(a^2+5)$
- 2. $5 (a^{2} + a)$ $5(a^2+a)$
- 3. $a (5 a + 5)$ $a(5a+5)$
- 4. $a (a + 5)$ $a(a+5)$
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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 $a^{2}$ $a^2$ : $a$ $a$ $\times a$ $times a$

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

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

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

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

$a [(a^{2} \div a) + (5 a \div a)]$ $a[(a^2diva)+(5adiva)]$

$=$ $=$ $a (a + 5)$ $a(a+5)$

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

4. Question
Factor.

$35 x + 42$ $35x+42$
- 1. $7 (5 x + 6)$ $7(5x+6)$
- 2. $7 (28 x + 35)$ $7(28x+35)$
- 3. $5 (7 x + 12)$ $5(7x+12)$
- 4. $14 (3 x + 4)$ $14(3x+4)$
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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 $35 x$ $35x$ : $5 \times$ $5times$ $7$ $7$ $\times x$ $times x$

Factors of $42$ $42$ : $7$ $7$ $\times 6$ $times6$

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

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

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

$7 [(35 x \div 7) + (42 \div 7)]$ $7[(35xdiv7)+(42div7)]$

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

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

5. Question
Factor.

$40 + 72 a$ $40+72a$
- 1. $5 (5 + 7 a)$ $5(5+7a)$
- 2. $3 (9 + 16 a)$ $3(9+16a)$
- 3. $8 (5 + 9 a)$ $8(5+9a)$
- 4. $6 (6 + 12 a)$ $6(6+12a)$
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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 $40$ $40$ : $8$ $8$ $\times 5$ $times5$

Factors of $72 a$ $72a$ : $8$ $8$ $\times 9 \times a$ $times9timesa$

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

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

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

$8 [(40 \div 8) + (72 a \div 8)]$ $8[(40div8)+(72adiv8)]$

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

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

Factor Expressions 1

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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5. Question

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Quizzes

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

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

		$a [(a^{2} \div a) + (5 a \div a)]$ $a[(a^2diva)+(5adiva)]$
	$=$ $=$	$a (a + 5)$ $a(a+5)$

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

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