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

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

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Answer 1 · 2016-01-03T14:44:30

$2 x^{2} + 9 x + 4 = (2 x + 1) (x + 4)$ $2x^2+9x+4=(2x+1)(x+4)$

Explanation:

$2 x^{2} + 9 x + 4$ $2x^2+9x+4$
First multiply the constant $4$ $4$ with the coefficient of $x$ $x^$ which is $2$ $2$

The result is $8$ $8$

Now find factors of $8$ $8$ such that they add up to the coefficient of $x$ $x$ here it is $+ 9$ $+9$ .

Let us list out the pairs which multiply to give $8$ $8$
These are $1, 8$ $1,8$ , $2, 4$ $2,4$ , $- 1, - 8$ $-1,-8$ and $- 2, - 4$ $-2,-4$

Let us check if these add up to $+ 9$ $+9$

$1 \times 8 = 8 and 1 + 8 = 9$ $1xx8=8 and 1+8 =9$ this works. Using this we shall split the middle term. $9 x = 1 x + 8 x$ $9x = 1x+8x$

$2 x^{2} + 9 x + 4$ $2x^2+9x+4$
$= 2 x^{2} + 1 x + 8 x + 4$ $=2x^2+1x+8x+4$ This is called splitting the middle term.
Now we would do factor by grouping.

$= (2 x^{2} + 1 x) + (8 x + 4)$ $=(2x^2+1x)+(8x+4)$

GCF from each group is taken out.

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

Now we have $(2 x + 1)$ $(2x+1)$ as the common factor, so it is factored out.

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

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

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