Question

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

Answer 1

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

Explanation:

`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.