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 $(5x-1)(5x+4)$.