How do you factor $12 x^{2} + 19 x + 5$ $12x^2+19x+5$ ?

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Answer 1 · 2015-05-02T07:12:53

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:

$N_{1} \cdot N_{2} = a \cdot c = 12 \cdot 5 = 60$ $N_1*N_2 = a*c = 12*5 = 60$
AND
$N_{1} + N_{2} = b = 19$ $N_1 +N_2 = b = 19$

After trying out a few numbers we get $N_{1} = 15$ $N_1 = 15$ and $N_{2} = 4$ $N_2 =4$

$15 \cdot 4 = 60$ $15*4 = 60$ , and $15 + 4 = 19$ $15+4= 19$

$12 x^{2} + 19 x + 5 = 12 x^{2} + 15 x + 4 x + 5$ $12x^2+19x+5 = 12x^2 + 15x +4x + 5$

$= 3 x (4 x + 5) + 1 (4 x + 5)$ $= 3x(4x + 5) + 1(4x+5)$

$4 x + 5$ $4x+5$ is a common factor to each of the terms

$= (4 x + 5) (3 x + 1)$ $=color(green)( (4x+5)(3x+1)$

How do you factor 12x^2+19x+512x2+19x+5 12x^2+19x+5?