Which correctly factored form of the function [tex]f(x) = 36 {x}^{2} + 15x - 6[/tex]can be used to identify the zeros?A. [tex]f(x) = (4x - 1)(3x + 2)[/tex]B. [tex]f(x) = (12x - 2)(3x + 3)[/tex]C. [tex]f(x) = 3(4x - 1)(3x + 2)[/tex]D. [tex]f(x) = 3(12x - 2)(3x + 3)[/tex]
Accepted Solution
A:
Answer:ƒ(x) = 3(4x - 1)(3x + 2)
Step-by-step explanation:Your function is: ƒ(x) = 36x² + 15x - 6
1. Remove the common factor
36x² + 15x - 6 = 3(12x² + 5x - 2)
2. Factor the quadratic
(a) Multiply the leading coefficient and the constant
12 × (-2) = -24
(b) Find two numbers that multiply to give -24 and add to give 5.
Possible pairs are 1, 24; 2, 12; 3, 8; 4, 6
One of the numbers must be negative. Start with the numbers near the end of the list.
By trial and error, you will find that 8 and -3 work:
-3 × 8 = -24 and -3 + 8 = 5
(b) Rewrite 5x as -3x + 8x
12x² - 3x + 8x - 2
(c) Factor by grouping the first two and the last two terms
(3x)(4x - 1) + 2(4x - 1) = (4x + 1)(3x + 2)
ƒ(x) = 3(4x -1)(3x + 2)
This is the correctly factored form that you can use to find the zeros.