How do you factor $3x^2+17x+10$ ?

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Answer 1 · 2015-08-10T15:19:31

$color(green)((3x+2)(x+5)$ is the factorised form of the expression.

$3x^2 +17x +10$

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

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

$N_1*N_2 = a*c = 3*10 =30$
and,
$N_1 +N_2 = b = 17$

After trying out a few numbers we get $N_1 = 15$ and $N_2 =2$
$15*2 = 30$ , and $15 +2=17$

$3x^2 +color(green)(17x) +10 =3x^2 +color(green)(15x +2x) +10$

$=3x(x+5)+2(x+5)$

$color(green)((3x+2)(x+5)$ is the factorised form of the expression.

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