Factorise a Polynomial 2

Years

Year 8

Products and Factors

Factorise a Polynomial

Factorise a Polynomial 2

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Question 1 of 5

1. Question
Factor.

$2 x y + 10 x z$ $2xy+10xz$
- 1. $2 x (y + 5 z)$ $2x(y+5z)$
- 2. $2 y (x + 5 x z)$ $2y(x+5xz)$
- 3. $2 (x y + 5 x z)$ $2(xy+5xz)$
- 4. $x (4 y + 5 z)$ $x(4y+5z)$
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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 $2 x y$ $2xy$ : $2$ $2$ $\times$ $times$ $x$ $x$ $\times y$ $times y$

Factors of $10 x z$ $10xz$ : $2$ $2$ $\times 5 \times$ $times5times$ $x$ $x$ $\times z$ $timesz$

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

GCF $=$ $=$ $2$ $2$ $\times$ $times$ $x$ $x$

$=$ $=$ $2 x$ $2x$

Finally, factor by placing $2 x$ $2x$ outside a bracket.

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

$2 x [(2 x y \div 2 x) + (10 x z \div 2 x)]$ $2x[(2xydiv2x)+(10xzdiv2x)]$

$=$ $=$ $2 x (y + 5 z)$ $2x(y+5z)$

$2 x (y + 5 z)$ $2x(y+5z)$
Question 2 of 5

2. Question
Factor.

$x y z - x y^{2}$ $xyz-xy^2$
- 1. $y z (x - y)$ $yz(x-y)$
- 2. $x (z - x)$ $x(z-x)$
- 3. $x y (z - y)$ $xy(z-y)$
- 4. $x z (x - y)$ $xz(x-y)$
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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 $x y z$ $xyz$ : $x$ $x$ $\times$ $times$ $y$ $y$ $\times z$ $times z$

Factors of $x y^{2}$ $xy^2$ : $x$ $x$ $\times$ $times$ $y$ $y$ $\times y$ $timesy$

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

GCF $=$ $=$ $x$ $x$ $\times$ $times$ $y$ $y$

$=$ $=$ $x y$ $xy$

Finally, factor by placing $x y$ $xy$ outside a bracket.

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

$x y [(x y z \div x y) - (x y^{2} \div x y)]$ $xy[(xyzdivxy)-(xy^2divxy)]$

$=$ $=$ $x y (z - y)$ $xy(z-y)$

$x y (z - y)$ $xy(z-y)$
Question 3 of 5

3. Question
Factor.

$6 a^{2} - 10 a + 14 b$ $6a^2-10a+14b$
- 1. $3 (4 a^{2} - 10 a + 2 b)$ $3(4a^2-10a+2b)$
- 2. $2 (a^{2} - 3 b + 4 b^{2})$ $2(a^2-3b+4b^2)$
- 3. $2 (3 a^{2} - 5 a + 7 b)$ $2(3a^2-5a+7b)$
- 4. $4 (2 a^{2} - 8 a + 6 b)$ $4(2a^2-8a+6b)$
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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 $6 a^{2}$ $6a^2$ : $2$ $2$ $\times 3 \times a \times a$ $times3timesatimesa$

Factors of $10 a$ $10a$ : $2$ $2$ $\times 5 \times a$ $times5timesa$

Factors of $14 b$ $14b$ : $2$ $2$ $\times 7 \times b$ $times7timesb$

All three terms have $2$ $2$ as their factor, so it is the GCF.

Finally, factor by placing $2$ $2$ outside a bracket.

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

$2 [(6 a^{2} \div 2) - (10 a \div 2) + (14 b \div 2)]$ $2[(6a^2div2)-(10adiv2)+(14bdiv2)]$

$=$ $=$ $2 (3 a^{2} - 5 a + 7 b)$ $2(3a^2-5a+7b)$

$2 (3 a^{2} - 5 a + 7 b)$ $2(3a^2-5a+7b)$
Question 4 of 5

4. Question
Factor.

$4 x^{2} - 6 x y$ $4x^2-6xy$
- 1. $2 x (2 x - 3 y)$ $2x(2x-3y)$
- 2. $2 x (3 x - 2 y)$ $2x(3x-2y)$
- 3. $3 x (3 x - 4 y)$ $3x(3x-4y)$
- 4. $2 x (3 x - 4 y)$ $2x(3x-4y)$
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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 $4 x^{2}$ $4x^2$ : $2$ $2$ $\times 2 \times$ $times2times$ $x$ $x$ $\times x$ $times x$

Factors of $6 x y$ $6xy$ : $2$ $2$ $\times 3 \times$ $times3times$ $x$ $x$ $\times y$ $times y$

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

GCF $=$ $=$ $2$ $2$ $\times$ $times$ $x$ $x$

$=$ $=$ $2 x$ $2x$

Finally, factor by placing $2 x$ $2x$ outside a bracket.

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

$2 x [(4 x^{2} \div 2 x) - (6 x y \div 2 x)]$ $2x[(4x^2div2x)-(6xydiv2x)]$

$=$ $=$ $2 x (2 x - 3 y)$ $2x(2x-3y)$

$2 x (2 x - 3 y)$ $2x(2x-3y)$
Question 5 of 5

5. Question
Factor.

$13 a b - a b^{2} - a^{2} b$ $13ab-ab^2-a^2b$
- 1. $a b (13 - b - a)$ $ab(13-b-a)$
- 2. $b (13 - a - a^{2})$ $b(13-a-a^2)$
- 3. $a (13 + b^{2} - a^{2})$ $a(13+b^2-a^2)$
- 4. $a (13 b - b^{2} - a b)$ $a(13b-b^2-ab)$
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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 $13 a b$ $13ab$ : $13 \times$ $13 times$ $a$ $a$ $\times$ $times$ $b$ $b$

Factors of $a b^{2}$ $ab^2$ : $a$ $a$ $\times$ $times$ $b$ $b$ $\times b$ $timesb$

Factors of $a^{2} b$ $a^2b$ : $a$ $a$ $\times a \times$ $timesatimes$ $b$ $b$

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

GCF $=$ $=$ $a$ $a$ $\times$ $times$ $b$ $b$

$=$ $=$ $a b$ $ab$

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

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

$a b [(13 a b \div a b) - (a b^{2} \div a b) - (a^{2} b \div a b)]$ $ab[(13abdivab)-(ab^2divab)-(a^2bdivab)]$

$=$ $=$ $a b (13 - b - a)$ $ab(13-b-a)$

$a b (13 - b - a)$ $ab(13-b-a)$

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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

GCF	$=$ $=$	$2$ $2$ $\times$ $times$ $x$ $x$
	$=$ $=$	$2 x$ $2x$

		$2 x [(2 x y \div 2 x) + (10 x z \div 2 x)]$ $2x[(2xydiv2x)+(10xzdiv2x)]$
	$=$ $=$	$2 x (y + 5 z)$ $2x(y+5z)$

GCF	$=$ $=$	$x$ $x$ $\times$ $times$ $y$ $y$
	$=$ $=$	$x y$ $xy$

		$x y [(x y z \div x y) - (x y^{2} \div x y)]$ $xy[(xyzdivxy)-(xy^2divxy)]$
	$=$ $=$	$x y (z - y)$ $xy(z-y)$

		$2 [(6 a^{2} \div 2) - (10 a \div 2) + (14 b \div 2)]$ $2[(6a^2div2)-(10adiv2)+(14bdiv2)]$
	$=$ $=$	$2 (3 a^{2} - 5 a + 7 b)$ $2(3a^2-5a+7b)$

		$2 x [(4 x^{2} \div 2 x) - (6 x y \div 2 x)]$ $2x[(4x^2div2x)-(6xydiv2x)]$
	$=$ $=$	$2 x (2 x - 3 y)$ $2x(2x-3y)$

GCF	$=$ $=$	$a$ $a$ $\times$ $times$ $b$ $b$
	$=$ $=$	$a b$ $ab$

		$a b [(13 a b \div a b) - (a b^{2} \div a b) - (a^{2} b \div a b)]$ $ab[(13abdivab)-(ab^2divab)-(a^2bdivab)]$
	$=$ $=$	$a b (13 - b - a)$ $ab(13-b-a)$