Question

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

Answer 1

`color(blue)((3x+1)(x+3)` is the factorised form for the expression.

Explanation:

`3x^2 +10x +3`

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*3 =9`
and,
`N_1 +N_2 = b = 10`

After trying out a few numbers we get:
`N_1 = 9` and `N_2 =1`
`9*1 = 9`, and `9+(1)= 10`

`3x^2 +color(blue)(10x) +3 = 3x^2 +color(blue)(9x+1x) +3`
`=3x(x+3)+1(x +3)`

`color(blue)((3x+1)(x+3)` is the factorised form for the expression.