# How do you factor 90y ^ { 2} - 21y - 45?

Jul 21, 2017

$\left(15 y + 9\right) \left(6 y - 5\right)$

#### Explanation:

$90 {y}^{2} - 21 y - 45$

Factorise.

$90 {y}^{2} - 75 y + 54 y - 45$

$15 y \left(6 y - 5\right) + 9 \left(6 y - 5\right)$

$\left(15 y + 9\right) \left(6 y - 5\right)$

Jul 21, 2017

3(5y + 3)(6y - 5)

#### Explanation:

Use the new AC Method to factor trinomial (Socratic, Google Search).
f() = 90y^2 - 21y - 45 = 3Z . Factor Z = (30x^2 - 7y - 15) = 30(y + p)(y + q) Converted trinomial: Z' = y^2 - 7y - 450 = (y + p')(y + q') Proceeding: Find p' and q', then, divide them by a = 30 Find 2 number p' and q', that have opposite signs, knowing the sum (- b = 7) and product (ac = -450). Use calculator to compose factor pairs of (-450) --> ...(15, -30)(18 - 25). This last sum is (-7 = b). Therefore, p' = 18 and q' = -25. Back to original Z  = (p')/a = 18/30 = 3/5$\mathmr{and}$q= (q')/a = -25/30 = - 5/6#
Factored form:
Z = 30(y + 3/5)(y - 5/6) = (5y + 3)(6y - 5)
Finally,
f(y) = 3(5y + 3)(6y - 5)