Question

What is the factored expression of 63x^2-3x-6

Answer 1

`3(3x-1)(7x +2)`

Explanation:

`63x^2-3x-6`

Suppose a generic quadratic equation

`ax^2 + bx + c`

To factor this equation, I need to find its roots. Then we use the quadratic formula of:

`(-b + √(b^2-4ac))/(2a)`

and

`(-b + √(b^2-4ac))/(2a)`

So, for the equation 63x ^ 2-3x-6 we have:

`(3 + √((-3)^2-4(63)(-6)))/(2(63)) = (1)/(3)`

and

`(3 - √((-3)^2-4(63)(-6)))/(2(63)) = (-2)/(7)`

So:

`(x-(1)/(3)) = 0\\\\(3x-1) = 0`

and

`(x - (-(2)/(7))) = 0\\\\(x+ (2)/(7)) = 0\\\\(7x +2) = 0`

Finally the polynomial is:

`(3x-1)(7x +2)`