How do you factor $10x^2+3x-4$ ?

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Answer 1 · 2015-08-10T15:29:12

$color(blue)((2x-1)( 5x +4)$ is the factorised form of the expression.

$10x^2+3x−4$

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:

$N_1*N_2 = a*c = 10*-4 = -40$
and,
$N_1 +N_2 = b = 3$

After trying out a few numbers we get $N_1 = 8$ and $N_2 =-5$
$8*-5 = -40$ , and $8+(-5)=3$

$10x^2+color(blue)(3x)−4 = 10x^2+color(blue)(8x - 5x)−4$

$=2x( 5x +4)−1(5x+4)$

$color(blue)((2x-1)( 5x +4)$ is the factorised form of the expression.

How do you factor 10x^2+3x-410x^2+3x-4?