How do you factor the expression 2x^2 +11x-9?

1 Answer
George C.
Sep 23, 2016

2x^2+11x-9 = 1/8(4x+11-sqrt(193))(4x+11+sqrt(193))

Explanation:

Note that if the - sign was a +, then this would factor with integer coefficients:

2x^2+11x+9 = (x+1)(2x+9)

To factor the given quadratic with a minus sign, we can complete the square, but to cut down on fractions, I would like to multiply through by 8 first, then divide through by 8 at the end...

8(2x^2+11x-9) = 16x^2+88x-72

color(white)(8(2x^2+11x-9)) = (4x)^2+2(11)(4x)+121-193

color(white)(8(2x^2+11x-9)) = (4x+11)^2-(sqrt(193))^2

color(white)(8(2x^2+11x-9)) = ((4x+11)-sqrt(193))((4x+11)+sqrt(193))

color(white)(8(2x^2+11x-9)) = (4x+11-sqrt(193))(4x+11+sqrt(193))

So:

2x^2+11x-9 = 1/8(4x+11-sqrt(193))(4x+11+sqrt(193))

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