Factoring trinomials (factor out the greatest common factor) 4x^2+22x+10?

1 Answer
Nghi N
Mar 1, 2018

2(x + 5)(2x + 1)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
#y = 4x^2 + 22x + 10 =# 4(x + p)(x + q)
Converted trinomial:
#ý = x^2 + 22x + 40 =# (x + p')(x + q').
Find p' and q' knowing the sum (22) and the product (40). They are: p' = 20 and q' = 2
Back to y, we get -->
#p = (p')/a = 20/4 = 5#
#q = (q')/a = 2/4#
Factored form
y = 4(x + 5)(x + 2/4) = (x + 5)(4x +2) = 2(x + 5)(2x + 1)#

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