determine the x-intercepts of the function f(x) = 12x^2 + 5x - 2

Answer 1

Hello, Holly.

finding x intercept means finding zeros or solving equation for x when y is 0

12x² + 5x - 2 = 0 we need to factor this equation to find x-intercepts.

the function is on Ax² + Bx +C form; since A is not 1 we need to multiply A and C

12*-2 = -24 we need to factor -24 but sum of these factors need to be B (in this case 5)

some factors of -24;

-24*1

12*-2

8*-3

6*-4

when you combine 8 and -3; you get 5; that's it.

So we can have 12x² + 8x - 3x - 2

12x² + 8x - 3x - 2 = 4𝑥(3𝑥+2)−1(3𝑥+2) when we group

since 3x +2 is common, answer will be

(3x+2)(4x -1)

hope that helps