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

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Answer 1 · 2016-04-03T10:58:52

$color(green)( (2x + 1 ) ( x - 3)$ 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#

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

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

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

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

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

How do you factor 2x^2 - 5x - 3 2x^2 - 5x - 3?