How do you factor 8m² -34m -9 ?

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Answer 1 · 2015-05-17T08:20:16

$8m^2- 34m - 9$

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

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

$N_1*N_2 = axxc = 8xx(-9)= -72$

And,

$N_1 +N_2 = b = -34$

After trying out a few numbers we get $N_1 = -36$ and $N_2 =2$
$(-36) xx 2 = -72$ , and $-36 +2 = -34$

$8m^2- 34m - 9 = 8m^2- 36m + 2m - 9$

$= 4m(2m - 9) + 1(2m - 9)$

$= (4m + 1) (2m - 9)$
$color(green)((4m + 1) (2m - 9) )$ is the Factorised form of $8m^2- 34m - 9$