could someone help me factor this?

Question

Factor the following problem completely. First factor out the greatest common factor, and then factor the remaining trinomial.

 

y⁴+4y³-21y²

Answer 1

 

 

Hi Seth,

 

First, if we factor out the common factor y²,

 

we get

 

     y⁴ + 4y³ - 21y²

 

          = y²(y² + 4y - 21).

 

Then, looking into the inside of parenthesis,

 

we need to figure out a pair of numbers

 

of which sum is 4 and product is -21.

 

The pair which meets the conditions is -3 and 7.

 

So, the expression in the parenthesis can be further factored

 

     y⁴ + 4y³ - 21y²
 
          = y²(y² + 4y - 21)

 

          = y²(y + 7)(y - 3).

 

Hope this helps.