Factor Expressions using GCF

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Question 1 of 7

1. Question
Factorise.

$40x^2+35x$
- 1. $10x(3x+4)$
- 2. $5x(8x+7)$
- 3. $4x(5x+6)$
- 4. $5x(2x+3x)$
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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 by using a factor tree.

Factors of $40x^2$ :

Factors of $35x$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $5$ $times$ $x$

$=$ $5x$

Finally, factorise by placing $5x$ outside a bracket.

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

$5x[(40x^2div5x)+(35xdiv5x)]$

$=$ $5x(8x+7)$

$5x(8x+7)$
Question 2 of 7

2. Question
Factorise.

$28x^2y^2-49xyz$
- 1. $7y(14x-21xz)$
- 2. $7xy(4xy-7z)$
- 3. $7xyz(4xy-7)$
- 4. $7x(21x+42z)$
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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 by using a factor tree.

Factors of $28x^2y^2$ :

Factors of $49xyz$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $7$ $times$ $x$ $times$ $y$

$=$ $7xy$

Finally, factorise by placing $7xy$ outside a bracket.

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

$7xy[(28x^2y^2div7xy)-(49xyzdiv7xy)]$

$=$ $7xy(4xy-7z)$

$7xy(4xy-7z)$
Question 3 of 7

3. Question
Factorise.

$8mp-16mt+2m^2$
- 1. $2m(6p-10t+2m)$
- 2. $4m(2p-4t+m)$
- 3. $2m(4p-8t+m)$
- 4. $4m(p-2t+m)$
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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 three terms by using a factor tree.

Factors of $8mp$ :

Factors of $16mt$ :

Factors of $2m^2$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $2$ $times$ $m$

$=$ $2m$

Finally, factorise by placing $2m$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $2m$ , then simplify.

$2m[(8mpdiv2m)-(16mtdiv2m)+(2m^2div2m)]$

$=$ $2m(4p-8t+m)$

$2m(4p-8t+m)$
Question 4 of 7

4. Question
Factorise.

$36a^2b-54ab^2c$
- 1. $18ab(2ab-3ac)$
- 2. $12ab(3a-4bc)$
- 3. $12ab(2a^2-3c)$
- 4. $18ab(2a-3bc)$
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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 by using a factor tree.

Factors of $36a^2b$ :

Factors of $54ab^2c$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $2$ $times$ $3$ $times$ $3$ $times$ $a$ $times$ $b$

$=$ $18ab$

Finally, factorise by placing $18ab$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $18ab$ , then simplify.

$18ab[(36a^2bdiv18ab)-(54ab^2cdiv18ab)]$

$=$ $18ab(2a-3bc)$

$18ab(2a-3bc)$
Question 5 of 7

5. Question
Factorise.

$9xy^2+18x^2y+12xy$
- 1. $3xy(3y+6x+4)$
- 2. $6xy(y+2x+3)$
- 3. $12xy(y+6x)$
- 4. $3xy(18xy+15y+15x)$
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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 three terms by using a factor tree.

Factors of $9xy^2$ :

Factors of $18x^2y$ :

Factors of $12xy$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $3$ $times$ $x$ $times$ $y$

$=$ $3xy$

Finally, factorise by placing $3xy$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $3xy$ , then simplify.

$3xy[(9xy^2div3xy)+(18x^2ydiv3xy)+(12xydiv3xy)]$

$=$ $3xy(3y+6x+4)$

$3xy(3y+6x+4)$
Question 6 of 7

6. Question
Factorise.

$24n-60mn-96n^2$
- 1. $12n(2-5m-8n)$
- 2. $6n(4-10m-16n)$
- 3. $8n(3-7m-12n)$
- 4. $9n(3-10m-12n)$
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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 three terms by using a factor tree.

Factors of $24n$ :

Factors of $60mn$ :

Factors of $96n^2$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $3$ $times$ $2$ $times$ $2$ $times$ $n$

$=$ $12n$

Finally, factorise by placing $12n$ outside a bracket.

Also, place the given polynomial inside the bracket with each term divided by $12n$ , then simplify.

$12n[(24ndiv12n)-(60mndiv12n)-(96n^2div12n)]$

$=$ $12n(2-5m-8n)$

$12n(2-5m-8n)$
Question 7 of 7

7. Question
Factorise.

$16pq^2+20p^2qv-24q^2$
- 1. $4q(8q+2pq^2-3q)$
- 2. $4q(4pq+5pv^2+10q)$
- 3. $2q(5pq-10p^2-6q)$
- 4. $4q(4pq+5p^2v-6q)$
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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 three terms by using a factor tree.

Factors of $16pq^2$ :

Factors of $20p^2qv$ :

Factors of $24q^2$ :

Collect the common factors and multiply them all to get the GCF.

GCF $=$ $2$ $times$ $2$ $times$ $q$

$=$ $4q$

Finally, factorise by placing $4q$ outside a bracket.

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

$4q[(16pq^2div4q)+(20p^2qvdiv4q)-(24q^2div4q)]$

$=$ $4q(4pq+5p^2v-6q)$

$4q(4pq+5p^2v-6q)$

Factor Expressions using GCF

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Quiz summary

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Quizzes

GCF	$=$	$2$ $times$ $3$ $times$ $3$ $times$ $a$ $times$ $b$
	$=$	$18ab$

		$3xy[(9xy^2div3xy)+(18x^2ydiv3xy)+(12xydiv3xy)]$
	$=$	$3xy(3y+6x+4)$

GCF	$=$	$3$ $times$ $2$ $times$ $2$ $times$ $n$
	$=$	$12n$

		$12n[(24ndiv12n)-(60mndiv12n)-(96n^2div12n)]$
	$=$	$12n(2-5m-8n)$

		$4q[(16pq^2div4q)+(20p^2qvdiv4q)-(24q^2div4q)]$
	$=$	$4q(4pq+5p^2v-6q)$

		$5x[(40x^2div5x)+(35xdiv5x)]$
	$=$	$5x(8x+7)$

		$7xy[(28x^2y^2div7xy)-(49xyzdiv7xy)]$
	$=$	$7xy(4xy-7z)$

		$2m[(8mpdiv2m)-(16mtdiv2m)+(2m^2div2m)]$
	$=$	$2m(4p-8t+m)$

		$18ab[(36a^2bdiv18ab)-(54ab^2cdiv18ab)]$
	$=$	$18ab(2a-3bc)$