Question

How do you factor `2x^2-5x+3`?

Answer 1

`color(blue)((2x-3)(x-1)` is the factorised form of the expression.

Explanation:

`2x^2 -5x +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 = 2*3 = 6`
and
`N_1 +N_2 = b = -5`

After trying out a few numbers we get `N_1 = -2` and `N_2 =-3`
`(-2)*(-3) = 6`, and `(-2)+(-3)= -5`

`2x^2color(blue)( -5x) +3 = 2x^2 color(blue)(-2x-3x) +3`

`=2x(x-1) -3(x-1)`

`color(blue)((2x-3)(x-1)` is the factorised form of the expression.

Answer 2

factor: `y = 2x^2 - 5x + 3`

Ans: (x - 1)(2x - 3)

Explanation:

Since a + b + c = 0, use the shortcut. One factor is (x - 1) and the other is `(x - c/a) = (x - 3/2)`
Factoring form: y = (x - 1)( 2x - 3)
The shortcut avoids the lengthy factoring by grouping.