How do you factor $5 y^{2} - 3 y - 2$ $5y^2-3y-2$ ?

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How do you factor $5 y^{2} - 3 y - 2$ $5y^2-3y-2$ ?

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Answer 1 · 2015-08-10T15:23:49

$= (5 y + 2) (y - 1)$ $= color(blue)((5y+2)(y-1)$

Explanation:

$5 y^{2} - 3 y - 2$ $5y^2−3y-2$

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 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 5 \cdot - 2 = - 10$ $N_1*N_2 = a*c = 5*-2 = -10$
and,
$N_{1} + N_{2} = b = - 3$ $N_1 +N_2 = b = -3$

After trying out a few numbers we get $N_{1} = - 5$ $N_1 = -5$ and $N_{2} = 2$ $N_2 =2$
$- 5 \cdot 2 = - 10$ $-5*2 = -10$ , and $2 + (- 5) = - 3$ $2+(-5)=-3$

$5 y^{2} - 3 y - 2 = 5 y^{2} - 5 y + 2 y - 2$ $5y^2−color(blue)(3y)-2 = 5y^2−color(blue)(5y+2y)-2$

$= 5 y (y - 1) + 2 (y - 1)$ $= 5y(y-1) +2(y-1)$

$= (5 y + 2) (y - 1)$ $= color(blue)((5y+2)(y-1)$

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How do you factor $5 y^{2} - 3 y - 2$ $5y^2-3y-2$ ?

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