How do you factor $4 x^{2} + 2 x - 20$ $4x^2+2x-20$ ?

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How do you factor $4 x^{2} + 2 x - 20$ $4x^2+2x-20$ ?

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Answer 1 · 2015-08-11T16:46:53

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

Explanation:

$4 x^{2} + 2 x - 20$ $4x^2+2x−20$

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

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

$N_{1} \cdot N_{2} = a \cdot c = 4 \cdot - 20 = - 80$ $N_1*N_2 = a*c = 4*-20 = -80$
and
$N_{1} + N_{2} = b = 2$ $N_1 +N_2 = b = 2$

After trying out a few numbers we get $N_{1} = 10$ $N_1 = 10$ and $N_{2} = - 8$ $N_2 =-8$
$10 \cdot (- 8) = - 80$ $10*(-8) = -80$ , and $10 + (- 8) = 2$ $10+(-8)= 2$

$4 x^{2} + 2 x - 20 = 4 x^{2} + 10 x - 8 x - 20$ $4x^2+color(blue)(2x)−20 =4x^2+color(blue)(10x -8x)−20$

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

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How do you factor $4 x^{2} + 2 x - 20$ $4x^2+2x-20$ ?

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