Factor Expressions 2

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Question 1 of 5

1. Question
Factor.

`2xy+10xz`
- `2x(y+5z)`
- `2(xy+5xz)`
- `x(4y+5z)`
- `2y(x+5xz)`
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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 `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`
- `xy(z-y)`
- `x(z-x)`
- `xz(x-y)`
- `yz(x-y)`
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Incorrect

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`
- `2(3a^2-5a+7b)`
- `4(2a^2-8a+6b)`
- `3(4a^2-10a+2b)`
- `2(a^2-3b+4b^2)`
Hint

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Correct

Exceptional!

Incorrect

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`
- `2x(2x-3y)`
- `2x(3x-2y)`
- `2x(3x-4y)`
- `3x(3x-4y)`
Hint

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Correct

Excellent!

Incorrect

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`
- `ab(13-b-a)`
- `a(13+b^2-a^2)`
- `a(13b-b^2-ab)`
- `b(13-a-a^2)`
Hint

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Correct

Fantastic!

Incorrect

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)`

Factor Expressions 2

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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``times``x`
	`=`	`2x`

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

GCF	`=`	`x``times``y`
	`=`	`xy`

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