Question

Which of the binomials below is a factor of this trinomial? ---- PLS EXPLAIN FOR ME?

6x^2-5x-25

Answer 1

(2x-5)(3x+5)

Can't show you how to do it, but I'll show proof and some explanations.

Proof:

(2x-5)(3x+5)
(2x)(3x) + (2x)(5) + (-5)(3x) + (-5)(5)
6x^2 + 10x - 15x - 25
6x^2 - 5x - 25

Explainations

(2x-5)(3x+5)

6x^2 comes from multiplying 2x and 3x.
-25 comes from multiplying 5 and -5.

For -5x, I just rearranged the terms until it would equal -5x (10x - 15x)

Answer 2

To factor this notable trinomial, you have to find two numbers that summes give -5 and multiplied give 6*(-25) = -150

Then let's call n1 and n2 the two numbers and a the number before x^2 (6)

ax^2+sx+fn = (ax + n1)(x + n2/a)

Numbers are -15 and +10

-15+10 = -5
-15*10 = -150

So

(6x-15)(x + 10/6)

Or write it as a sum

6x^2 + 10x - 15x - 25

And factor

6x^2 + 10x = 2x(3x+5)

-15x-25 = -5(3x+5)

(2x-5)(3x+5)