Question

How do you factor this trinomial: 5x^2-23x+12 step by step?

Answer 1

Find two numbers that multiply to 5*12 = 60 and add to -23

Answer 2

okay thank you

Answer 3

tell me what you get

Answer 4

(x-3)(x-20)?

Answer 5

-3 and -20 are the two numbers, but that's not the correct factorization

Answer 6

that trick only works when the leading coefficient is 1

Answer 7

Then what do I do?

Answer 8

Replace -23x with -3x-20x to get


5x^2-23x+12

5x^2-3x-20x+12


Now factor by grouping

Answer 9

By grouping?

Answer 10

Are you familiar with that technique?

Answer 11

No, not really.

Answer 12

Alright, here's how you factor this by grouping

5x^2-23x+12

5x^2-3x-20x+12

(5x^2-3x)+(-20x+12)

x(5x-3)+(-20x+12)

x(5x-3)-4(5x-3)

(x-4)(5x-3)

Answer 13

Thank you!

Answer 14

np