How do you factor $3 f^{2} - 2 f - 21$ $3f^2-2f-21$ ?

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How do you factor $3 f^{2} - 2 f - 21$ $3f^2-2f-21$ ?

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Answer 1 · 2016-04-14T08:26:49

$(3 f + 7) (f - 3)$ $color(blue)( (3f + 7 ) ( f - 3 )$ is the factorised form of the equation.

Explanation:

$3 f^{2} - 2 f - 21$ $3f^2 - 2f - 21$

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

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

$N_{1} \cdot N_{2} = a \cdot c = 3 \cdot - 21 = - 63$ $N_1*N_2 = a*c = 3*-21 = -63$

AND

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

After trying out a few numbers we get $N_{1} = - 9$ $N_1 = -9$ and $N_{2} = 7$ $N_2 =7$
$7 \cdot (- 9) = - 63$ $7*(-9 )= -63$ , and $7 + (- 9) = - 2$ $7 + (-9)= -2$

$3 f^{2} - 2 f - 21 = 3 f^{2} - 9 f + 7 f - 21$ $3f^2 - 2f - 21 = 3f^2 - 9f + 7f - 21$

$= 3 f (f - 3) + 7 (f - 3)$ $= 3f ( f - 3 ) + 7 ( f- 3 )$

$= (3 f + 7) (f - 3)$ $= (3f + 7 ) ( f - 3 )$

$(3 f + 7) (f - 3)$ $color(blue)( (3f + 7 ) ( f - 3 )$ is the factorised form of the equation.

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How do you factor $3 f^{2} - 2 f - 21$ $3f^2-2f-21$ ?

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