How do you factor the trinomial $2x^2 +11x + 9$ ?

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Answer 1 · 2016-05-16T16:58:35

$color(blue)( (2x + 9) (x + 1)$ is the factorised form of the expression.

$2x^2 + 11x + 9$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 2 * 9 = 18$

AND

$N_1 +N_2 = b = 11$

After trying out a few numbers we get $N_1 = 9$ and $N_2 =2$

$9 * 2 = 18$ , and $2 + 9 = 11$

$2x^2 + 11x + 9 = 2x^2 + 2x + 9x + 9$

$= 2x(x + 1) + 9( x + 1 )$

$(x+1)$ is a common factor to each of the terms
$= color(blue)( (2x + 9) (x + 1)$

How do you factor the trinomial 2x^2 +11x + 92x^2 +11x + 9?