Question

Help!! To factor the polynomial 25x^2 +15x - 4, find two numbers whose product is _ and whose sum is _.

Answer 1

Compare given polynomial
`25x^2 +15x - 4` with quadratic polynomial

`ax^2+bx+c`, we get:

a=25, b=15, c=-4

Step1: find product of a and c which is 25*-4= -100

Step2: find two numbers whose product is ac and sum is b that is product is -100 and sum is 15

We see that 20 and -5 satisfy condition of step2.

Step3: Break middle term of
`25x^2 +15x - 4` into two parts -100x and +15x then proceed factor by grouping.

`25x^2 +15x - 4`

`=25x^2 +20x -5x- 4`

`=5x(5x+4) -1(5x+4)`

`=(5x-1)(5x+4)`

Hence final answer is
`(5x-1)(5x+4)`.