Question

How do you factor `4x^2-16x+15`?

Answer 1

`4x^2-16x+15=(2x-3)(2x-5)`

Explanation:

To factorize `ax^2+bx+c`, one should split middle term in two parts, so that their product is `ac` and sum is `b`.

Hence in `4x^2-16x+15`, while the product should be `4xx15=60`, sum should be `-16`. It is apparent that these are `-6` and `-10`.

Hence `4x^2-16x+15`

= `4x^2-10x-6x+15`

= `2x(2x-5)-3(2x-5)`

= `(2x-3)(2x-5)`