Factorise a Polynomial 2

Years

Year 10

Products and Factors

Factorise a Polynomial

Factorise a Polynomial 2

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 5

1. Question
Factor.

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

Help Video
Correct

Well Done!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

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 $2xy$ : $2$ $times$ $x$ $times y$

Factors of $10xz$ : $2$ $times5times$ $x$ $timesz$

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

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

$=$ $2x$

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

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

$2x[(2xydiv2x)+(10xzdiv2x)]$

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

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

2. Question
Factor.

$xyz-xy^2$
- 1. $xy(z-y)$
- 2. $x(z-x)$
- 3. $xz(x-y)$
- 4. $yz(x-y)$
Hint

Help Video
Correct

Nice Job!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

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 $xyz$ : $x$ $times$ $y$ $times z$

Factors of $xy^2$ : $x$ $times$ $y$ $timesy$

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

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

$=$ $xy$

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

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

$xy[(xyzdivxy)-(xy^2divxy)]$

$=$ $xy(z-y)$

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

3. Question
Factor.

$6a^2-10a+14b$
- 1. $2(a^2-3b+4b^2)$
- 2. $3(4a^2-10a+2b)$
- 3. $2(3a^2-5a+7b)$
- 4. $4(2a^2-8a+6b)$
Hint

Help Video
Correct

Exceptional!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

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 $6a^2$ : $2$ $times3timesatimesa$

Factors of $10a$ : $2$ $times5timesa$

Factors of $14b$ : $2$ $times7timesb$

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

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

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

$2[(6a^2div2)-(10adiv2)+(14bdiv2)]$

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

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

4. Question
Factor.

$4x^2-6xy$
- 1. $2x(2x-3y)$
- 2. $2x(3x-2y)$
- 3. $2x(3x-4y)$
- 4. $3x(3x-4y)$
Hint

Help Video
Correct

Excellent!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

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 $4x^2$ : $2$ $times2times$ $x$ $times x$

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

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

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

$=$ $2x$

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

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

$2x[(4x^2div2x)-(6xydiv2x)]$

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

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

5. Question
Factor.

$13ab-ab^2-a^2b$
- 1. $b(13-a-a^2)$
- 2. $a(13b-b^2-ab)$
- 3. $a(13+b^2-a^2)$
- 4. $ab(13-b-a)$
Hint

Help Video
Correct

Fantastic!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

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 $13ab$ : $13 times$ $a$ $times$ $b$

Factors of $ab^2$ : $a$ $times$ $b$ $timesb$

Factors of $a^2b$ : $a$ $timesatimes$ $b$

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

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

$=$ $ab$

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

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

$ab[(13abdivab)-(ab^2divab)-(a^2bdivab)]$

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

$ab(13-b-a)$

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Well Done!

2. Question

Hint

Nice Job!

3. Question

Hint

Exceptional!

4. Question

Hint

Excellent!

5. Question

Hint

Fantastic!

Quizzes

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

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

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

		$xy[(xyzdivxy)-(xy^2divxy)]$
	$=$	$xy(z-y)$