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

Answer:

(x+5) is the final answer.

Step-by-step 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.