How do you factor $2 y^{2} + 7 y + 6$ $2y^2+7y+6$ ?

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How do you factor $2 y^{2} + 7 y + 6$ $2y^2+7y+6$ ?

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Answer 1 · 2015-05-30T13:06:26

$2 y^{2} + 7 y + 6$ $2y^2+7y+6$

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like $a y^{2} + b y + c$ $ay^2 + by + c$ , we need to think of two numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 2.6 = 12$ $N_1*N_2 = a*c = 2.6 = 12$
and
$N_{1} + N_{2} = b = 7$ $N_1 +N_2 = b = 7$
After trying out a few numbers we get $N_{1} = 3$ $N_1 = 3$ and $N_{2} = 4$ $N_2 =4$
$3 \cdot 4 = 12$ $3*4 = 12$ , and $3 + 4 = 7$ $3+4= 7$

$2 y^{2} + 7 y + 6 = 2 y^{2} + 4 y + 3 y + 6$ $2y^2+7y+6 = 2y^2+4y +3y +6$
$= 2 y^{2} + 4 y + 3 y + 6$ $=2y^2+4y +3y +6$
$= 2 y (y + 2) + 3 (y + 2)$ $=2y(y+2) +3(y +2)$
$= (2 y + 3) (y + 2)$ $=color(green)((2y+3)(y+2)$

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How do you factor $2 y^{2} + 7 y + 6$ $2y^2+7y+6$ ?

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