How do you factor -2x ^ 2 + 7x -3?

May 7, 2015

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

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = - 2 \cdot - 3 = 6$
AND
${N}_{1} + {N}_{2} = b = 7$

After trying out a few numbers we get ${N}_{1} = 6$ and ${N}_{2} = 1$

$6 \cdot 1 = 6$, and $6 + 1 = 7$

$- 2 {x}^{2} + 7 x - 3 = - 2 {x}^{2} + 6 x + x - 3$

$= - 2 x \left(x - 3\right) + 1 \left(x - 3\right)$

$x - 3$ is a common factor to each of the terms

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