Question

Factor the expression P^4+3p^3-10p^2

Answer 1

`p^2(p+5)(p-2)`

Explanation:

To begin factoring the expression
`p^4+3p^3-10p^2`, we use the GCF or greatest common factor. The greatest common factor is the greatest number that will divide into two or more values. We start to find it by factoring each term:

`p^4=p*p*p*p`

`3p^3: 3*p*p*p`

`-10p^2: -10*p*p`

Remember -10 can factor into smaller numbers but since it doesn't have common factors with the others, we've chosen to leave it as -10.

We notice the only common factors bare p*p or
`p^2`.

We write in the form p^2(____+_____+_____). We find the inside of the parenthesis by dividing each term by p^2.

`(p^4)/(p^2) =p^2`

`(3p^3)/(p^2) =3p`

`(-10p^2)/(p^2)=-10`

`p^2(p^2+3p-10)`.

We are not finished yet. We have a trinomial (3 terms) which also factors. We factor by splitting the middle term 3p into factors of -10 which add to 3.

--10 = 5 * -2

3p= 5p +-2p

We write
`p^2(p+5)(p-2)`.