Question

Factor the trinomial 4x2+23x-6

Answer 1

Trinomials can be factored three different ways: By grouping, With quadratic formula, Completing the square.

Quadratic formula hard to memorize but always works. Its template is:
`x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac } }{2a}`

To make quadratic formula work, we need to put the equation into the standard form. In this case, it's already in that form.
`a=4, b=23, c=-6`.

When we plug them in:
`x = \frac{- 23 \pm \sqrt{ {23}^(2) - 4 * 4 * ( - 6) } }{2 * 4}`

Simplify:

`x = ( - 23 \pm√(529 + 96) )/(8)`

`x = ( - 23\pm √(625) )/(8)`

`x = ( - 23 \pm25 )/(8)`

Branch out the plus-minus sign:

`x = ( - 23 + 25)/(8) \: \: \: \: \:x = ( - 23 - 25)/(8)`

`x = (2)/(8) \: \: \: \: \:x = ( - 48)/(8)`

`x = (1)/(4) \: \: \: \: \:x = - 6`

So it's roots are
`(1)/(4) , -6`.

Roots of a polynomial are the values which made the equation equal to 0. To make this, we need to write the factored form as
`(x - (1)/(4) )(x + 6)`

And because
`- (1)/(4)` is a fraction, we need to get rid of it. We can do this by multiplying the left side with 4 and our final answer would be
`(4x - 1)(x + 6)`.