Compare given polynomial [tex] 25x^2 +15x - 4 [/tex] with quadratic polynomial
[tex] ax^2+bx+c [/tex], 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 [tex] 25x^2 +15x - 4 [/tex] into two parts -100x and +15x then proceed factor by grouping.
[tex] 25x^2 +15x - 4 [/tex]
[tex] =25x^2 +20x -5x- 4 [/tex]
[tex] =5x(5x+4) -1(5x+4) [/tex]
[tex] =(5x-1)(5x+4) [/tex]
Hence final answer is [tex] (5x-1)(5x+4) [/tex].
