Question

How do you factor `-2x^2 + 1x + 1`?

Answer 1

• Set the expression = 0 and use the ABC formula
• Find factors by using `(x - x_1)(x-x_2)`
  `-2x^2 + x + 1 = (x+1/2)(x-1)`

Explanation:

Start by setting the expression equal to zero, then use the ABC-formula.

The ABC-formula is:
`(-b+-sqrt(b^2 - 4ac))/(2a)`

Insert the values for a, b and c (which are the coefficients(red) in your expression: `color(red)(-2)x^2 + color(red)(1)x + color(red)(1)`

`x =(-1 +- sqrt(1^2 - 4 * (-2) * 1)) / (2*(-2)) to (-1 +- sqrt(1+8)) / (-4) to (-1+-3)/-4`

`x_1 = (-1 + 3)/-4= 2/-4 = -1/2`

`x_2 = (-1 - 3)/-4= (-4) /(-4) = 1`

Put these values into `(x-x_1)(x-x_2)`

`(x-(-1/2))(x-1)`
`(x+1/2)(x-1)`