# How do you factor the expression 42x^2+77x+21?

Mar 10, 2016

y = 7(3x + 1)(2x + 3)

#### Explanation:

Use the systematic new AC Method to factor trinomials (Google, Yahoo)
$y = 42 {x}^{2} + 77 x + 21 =$ 42(x + p)(x + q)
Converted trinomial: $y ' = {x}^{2} + 77 x + 882 =$(x + p')(x + q').
p' and q' have same sign, since ac > 0.
Compose factor pairs of (ac = 882) --> ...(9, 98)(14, 63). This sum is
77 = b. Then p' = 14 and q' = 63.
Back to original trinomial: $p = \frac{p '}{a} = \frac{14}{42} = \frac{1}{3}$ and q = (q')/a = = 63/42 = 9/6 = 3/2.
Factored form $y = 42 \left(x + \frac{1}{3}\right) \left(x + \frac{3}{2}\right) = 7 \left(3 x + 1\right) \left(2 x + 3\right)$