Question

Which of the following is a factor of 2x^4 + 20x^3 + 50x^2?

A. 2x^3
B. x^4
C. x+4
D. x+5

Answer 1

D. x + 5

Explanation:

2x^4 + 20x^3 + 50x^2

= 2x^2 (x^2 + 10x + 25)

= 2x^2 (x + 5)^2

= 2x^2 (x + 5) (x + 5)

Answer

D. x + 5

Answer 2

For this case we have the following expression:

`2x ^ 4 + 20x ^ 3 + 50x ^ 2`

It is observed that we can extract common factor
`2x ^ 2`, since it is common in the three terms:

`2x ^ 2 (x ^ 2 + 10x + 25) =`

If we factor the expression into parentheses, we must look for two numbers that add 10 and multiply 25. These are: 5 and 5.

Rewriting the expression we have:

`2x ^ 2 ((x + 5) (x + 5))`

Thus, one of the factors of the original expression is
`x + 5`.

Answer:

Option D