How do you factor #2x^2+9x+4#?

1 Answer
Sudip Sinha
Aug 8, 2015

# (2x + 1) (x + 4) #

Explanation:

The idea is to break down the middle term into two monomials which can be used in the factorisation process. Note that # 2 * 4 = 8 = 8 * 1 #, and that we may write # 9 = 8 + 1 #, which may help us in the process.

Let us write:
# 2x^2 + 9x + 4 #
# = 2x^2 + 8x + x + 4 #
# = 2x(x + 4) + (x + 4) #
# = (2x + 1) (x + 4) #

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