Question

Which is a factor of 2x^2y^4 – 10x^2y + 14y^3 – 70 ?

Answers: y^3 – 2
x^2y + 7
x^2 – 1
x^2y^2 + 2

Answer 1

2x^2y^4-10x^2y+14y^3-70 ... Start with the given expression



(2x^2y^4-10x^2y)+(14y^3-70) ... Group like terms



2x^2y(y^3-5)+14(y^3-5) ... Factor out the GCF 2x^2y out of the first group. Factor out the GCF 14 out of the second group



(2x^2y+14)(y^3-5) ... Since we have the common term y^3-5, we can combine like terms



2(x^2y+7)(y^3-5) ... Now factor out the GCF 2 from the first group



So 2x^2y^4-10x^2y+14y^3-70 factors to 2(x^2y+7)(y^3-5)



In other words, 2x^2y^4-10x^2y+14y^3-70=2(x^2y+7)(y^3-5)



So the answer is choice B