How do you factor the trinomial $2x^2 - 5x -3$ ?

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Answer 1 · 2015-12-06T13:06:28

$color(blue)((2x+1) (x-3)$ is the factorised form of the expression.

$2x^2 -5x-3$

\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:

$N_1*N_2 = a*c = 2*-3 = -6$

AND

$N_1 +N_2 = b = -5$

After trying out a few numbers we get $N_1 = -6$ and $N_2 =1$

$-6*1 = -6$ , and $1+(-6)= -5$

$2x^2 color(blue)(-5x)-3 = 2x^2 color(blue)(-6x +1x)-3$

$=2x(x-3) +1 (x-3)$

$color(blue)(=(2x+1) (x-3)$

How do you factor the trinomial 2x^2 - 5x -32x^2 - 5x -3?