Question

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

A) x2y2 + 2
B) x2y + 7
C) y3 − 2
D) x2 − 1

Answer 1

B) x^2y + 7

Explanation:

we are given

`2x^2y^4-10x^2y+14y^3-70`

We can use grouping method to factor it

`(2x^2y^4-10x^2y)+(14y^3-70)`

`(2x^2y* y^3-5* 2x^2y)+(14y^3-14* 5)`

now, we can factor common terms

`2x^2y(y^3-5)+14(y^3-5)`

`(y^3-5)(2x^2y+14)`

so, we get

`2x^2y^4-10x^2y+14y^3-70=(y^3-5)(2x^2y+14)`

`2x^2y^4-10x^2y+14y^3-70=(y^3-5)2(x^2y+7)`

`2x^2y^4-10x^2y+14y^3-70=2(y^3-5)(x^2y+7)`

we can see that x^2y+7 is one of factor