How do you factor $3 x^{2} + 7 x + 2$ $3x^2+7x+2$ ?

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Answer 1 · 2016-05-16T17:10:39

$(3 x + 1) (x + 2)$ $color(green)((3x + 1 ) (x + 2)$ is the factorised form of the expression.

$3 x^{2} + 7 x + 2$ $3x^2 + 7x + 2$

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

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

$N_{1} \cdot N_{2} = a \cdot c = 3 \cdot 2 = 6$ $N_1*N_2 = a*c = 3*2 = 6$

AND

$N_{1} + N_{2} = b = 7$ $N_1 +N_2 = b = 7$

After trying out a few numbers we get $N_{1} = 6$ $N_1 = 6$ and $N_{2} = 1$ $N_2 =1$

$6 \cdot 1 = 6$ $6*1 = 6$ , and $6 + 1 = 7$ $6 + 1 = 7$

$3 x^{2} + 7 x + 2 = 3 x^{2} + 6 x + 1 x + 2$ $3x^2 + 7x + 2 = 3x^2 + color(blue)( 6x + 1 x ) + 2$

$= 3 x (x + 2) + 1 (x + 2)$ $= 3x(x + 2) + 1 (x + 2 )$

$(x + 2)$ $(x + 2 )$ is a common factor to each of the terms

$= (3 x + 1) (x + 2)$ $= color(green)((3x + 1 ) (x + 2)$

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