How do you factor completely $2 x^{2} - x - 10$ $2x^2-x-10$ ?

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How do you factor completely $2 x^{2} - x - 10$ $2x^2-x-10$ ?

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Answer 1 · 2016-05-23T13:11:39

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

Explanation:

$2 x^{2} - x - 10$ $2x^2 - x - 10$

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:

$N_{1} \cdot N_{2} = a \cdot c = 2 \cdot (- 10) = - 20$ $N_1*N_2 = a*c = 2*(-10) = -20$

AND

$N_{1} + N_{2} = b = - 1$ $N_1 +N_2 = b = -1$

After trying out a few numbers we get $N_{1} = - 5$ $N_1 = -5$ and $N_{2} = 4$ $N_2 = 4$
$4 \cdot (- 5) = - 20$ $4* (-5) = -20$ , and $4 + (- 5) = - 1$ $4+(-5)= -1$

$2 x^{2} - x - 10 = 2 x^{2} + 4 x - 5 x - 10$ $2x^2 - x - 10 = 2x^2 + 4x- 5x - 10$

$= 2 x (x + 2) - 5 (x + 2)$ $= 2x(x +2) - 5(x + 2)$

$(x + 2)$ $(x+2)$ is a common factor to each of the terms

$= (2 x - 5) (x + 2)$ $= color(blue)( (2x - 5) (x +2)$

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How do you factor completely $2 x^{2} - x - 10$ $2x^2-x-10$ ?

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How do you factor completely $2 x^{2} - x - 10$ $2x^2-x-10$ ?