Which of the following is a factor of 2x^(4) + 22xx^(3) + 60xx^(2)? x^(3) x^(4) x + 4 x + 5

Question

Which of the following is a factor of 2
`x^(4)` + 22x
`x^(3)` + 60x
`x^(2)`?


`x^(3)`


`x^(4)`

x + 4

x + 5

Answer 1

`2x^4+22x^3+60x^2=2x^2(x^2+11x+30)=2x^2(x^2+6x+5x+30)\\\\=2x^2[x(x+6)+5(x+6)]=2x^2(x+6)(x+5)\\\\Answer:\ x+5`

Answer 2

(x+5) is the final answer.

Explanation:

We have to find the factors of
`2x^4+22x^3+60x^2`

Then select correct choice or choices from the given options.

`2x^4+22x^3+60x^2`

`=2x^2(x^2+11x+30)`

`=2x^2(x^2+6x+5x+30)`

`=2x^2(x(x+6)+5(x+6))`

`=2x^2((x+5)(x+6))`

`=2x^2(x+5)(x+6)`

From above factors, we see that only (x+5) is correct.

Hence (x+5) is the final answer.