Question

One factor of 2y^4 - 20y^2 + 50 is

A. y^2 - 5
B. y^2 + 5
C. 2y^2 - 5
D. 2y - 5
E. y - 5

Answer 1

To find a factor of the polynomial 2y^4 - 20y^2 + 50, we can factor out the greatest common factor (GCF) from each term. The GCF of 2y^4, -20y^2, and 50 is 2. So, we can factor out 2:

2(y^4 - 10y^2 + 25)

Now, we have a quadratic expression inside the parentheses, which can be factored further. It's a perfect square trinomial:

2(y^2 - 5)^2

So, one factor of the polynomial is (y^2 - 5).

Now, let's check the options:

A. y^2 - 5

B. y^2 + 5

C. 2y^2 - 5

D. 2y - 5

E. y - 5

The correct option is A. y^2 - 5.

Explanation: