How do you factor $2 x^{2} + 9 x + 4$ $2x^2+9x+4$ ?

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How do you factor $2 x^{2} + 9 x + 4$ $2x^2+9x+4$ ?

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Answer 1 · 2015-08-08T06:29:02

$(2 x + 1) (x + 4)$ $(2x + 1) (x + 4)$

Explanation:

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

Let us write:
$2 x^{2} + 9 x + 4$ $2x^2 + 9x + 4$
$= 2 x^{2} + 8 x + x + 4$ $= 2x^2 + 8x + x + 4$
$= 2 x (x + 4) + (x + 4)$ $= 2x(x + 4) + (x + 4)$
$= (2 x + 1) (x + 4)$ $= (2x + 1) (x + 4)$

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How do you factor $2 x^{2} + 9 x + 4$ $2x^2+9x+4$ ?

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How do you factor $2 x^{2} + 9 x + 4$ $2x^2+9x+4$ ?