Factor completely

Question

25x⁵ + 65x⁴ - 80x³

 

factor completely

 

I came up with

 

5x³(5x² + 13x + 16)

 

am I right??>

Answer 1

25x⁵ + 65x⁴ - 80x³

 

Your answer of 5x³(5x² + 13x + 16) is almost correct.

Your last term was a negative so this should be

5x³(5x² + 13x - 16).

 

As Jacoby B. said, you need to check to see if

(5x²+ 13x - 16) is factorable.

 

Multiply the coefficient of the squared term, 5, by the

constant, -16.... 5(-16) = -80.

If there are factors of -80 that add to 13, the coefficient

of the x term, then this can be factored by grouping.

 

                   -80                         80-1=79

              2            40                 40-2 = 38

           2          2         20           20-4 = 16

         2          2        2       10     10-8 = 2

     2          2        2        2      5  16-5=11

 

The prime factors of -80 are -(2*2*2*2*5)

There is no way to add factors of this to make 13, thus

the trinomial is not further factorable and your answer is:

 

5x³(5x² + 13x - 16)

Answer 2

You can factored the trinomial you  came up with. It should be: 

 

5x^3(5x-4)(x+4) 

 

You can check this answer by multiplying the above and you should come up with the starting polynomial.