Factorise a Polynomial (HCF)

Years

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 7

1. Question
Factorise.

$40x^2+35x$
- 1. $5x(2x+3x)$
- 2. $4x(5x+6)$
- 3. $5x(8x+7)$
- 4. $10x(3x+4)$
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 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. $7x(21x+42z)$
- 3. $7xy(4xy-7z)$
- 4. $7xyz(4xy-7)$
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 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. $4m(2p-4t+m)$
- 2. $2m(6p-10t+2m)$
- 3. $2m(4p-8t+m)$
- 4. $4m(p-2t+m)$
Hint

Help Video
Correct

Keep Going!
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 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. $12ab(2a^2-3c)$
- 2. $18ab(2a-3bc)$
- 3. $18ab(2ab-3ac)$
- 4. $12ab(3a-4bc)$
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 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. $3xy(18xy+15y+15x)$
- 4. $12xy(y+6x)$
Hint

Help Video
Correct

Correct!
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 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. $9n(3-10m-12n)$
- 4. $8n(3-7m-12n)$
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 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. $2q(5pq-10p^2-6q)$
- 2. $4q(4pq+5pv^2+10q)$
- 3. $4q(8q+2pq^2-3q)$
- 4. $4q(4pq+5p^2v-6q)$
Hint

Help Video
Correct

Great Work!
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 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.

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

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

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

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Fantastic!

2. Question

Hint

Excellent!

3. Question

Hint

Keep Going!

4. Question

Hint

Nice Job!

5. Question

Hint

Correct!

6. Question

Hint

Well Done!

7. Question

Hint

Great Work!

Quizzes

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

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

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

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

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

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

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

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

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