Question

Which is a factor of 2x2y4 − 10x2y + 14y3 − 70?

Answer 1

2(y³ -5) (x²y+7) This is the correct answer

Answer 2

Given expression:
`2x^2y^4 - 10x^2y + 14y^3 - 70.`

We need to factor it.

`\mathrm{Rewrite\:}14\mathrm{\:as\:}7\cdot \:2`

`\mathrm{Rewrite\:}70\mathrm{\:as\:}35\cdot \:2`

`\mathrm{Rewrite\:}10\mathrm{\:as\:}5\cdot \:2`

`\mathrm{Factor\:out\:common\:term\:}2`

`=2\left(x^2y^4+7y^3-5x^2y-35\right)`

Makeing it into two groups.

`=\left(x^2y^4-5x^2y\right)+\left(7y^3-35\right)`

`\mathrm{Factor\:out\:}7\mathrm{\:from\:}7y^3-35\mathrm{:\quad }7\left(y^3-5\right)`

`\mathrm{Factor\:out\:}x^2y\mathrm{\:from\:}x^2y^4-5x^2y\mathrm{:\quad }x^2y\left(y^3-5\right)`

`=7\left(y^3-5\right)+x^2y\left(y^3-5\right)`

`\mathrm{Factor\:out\:common\:term\:}y^3-5`

`=\left(y^3-5\right)\left(x^2y+7\right)`

`2\left(x^2y^4+7y^3-5x^2y-35\right) =\left(y^3-5\right)\left(x^2y+7\right)`.

Therefore, final factored form is
`2\left(y^3-5\right)\left(x^2y+7\right).`