How do you factor the trinomial $5 r + r^{2} - 14$ $5r + r^2 - 14$ ?

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How do you factor the trinomial $5 r + r^{2} - 14$ $5r + r^2 - 14$ ?

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Answer 1 · 2016-03-25T18:04:46

$(r - 2) (r + 7)$ $color(green)( (r -2) ( r + 7 )$ is the factorised form of the equation.

Explanation:

$r^{2} + 5 r - 14$ $r^2 + 5r -14$

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

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

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot (- 14) = - 14$ $N_1*N_2 = a*c = 1* (- 14) = -14$

AND

$N_{1} + N_{2} = b = 5$ $N_1 +N_2 = b = 5$

After trying out a few numbers we get $N_{1} = 7$ $N_1 = 7$ and $N_{2} = - 2$ $N_2 =-2$
$7 \cdot (- 2) = - 14$ $7*(-2) = -14$ , and $7 + (- 2) = 5$ $7+(-2)= 5$

$r^{2} + 5 r - 14 = r^{2} + 7 r - 2 r - 14$ $r^2 + color(green)( 5r) -14 = r^2 + color(green)(7r -2r) -14$

$= r (r + 7) - 2 (r + 7)$ $= r ( r+7 ) -2 ( r + 7)$

$= (r - 2) (r + 7)$ $= color(green)( (r -2) ( r + 7 )$

$(r - 2) (r + 7)$ $color(green)( (r -2) ( r+7 )$ is the factorised form of the equation.

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How do you factor the trinomial $5 r + r^{2} - 14$ $5r + r^2 - 14$ ?

1 Answer

Explanation:

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