Question

Select all factors of the following polynomial: 4p3 + 36p2 + 32p

Answer 1

We can follow the factors as follows:

$4p\cdot(p^2+9p+8)$

We have now to factor the second-order polynomial. For this, we can use the Quadratic Formula to find the roots and then factor them, or we can try to find two numbers that:

1. If we sum them, we have 9.

2. If we multiply them, we have 8.

In this case, both numbers are 1 and 8, since:

1+8 = 9

1*8 = 8

Then, the factors are:

$4p\cdot(p+1)\cdot(p+8)$

Therefore, the factors of the original polynomial are:

4p, (p+1) and (p + 8).