What is the factored form of the quadratic expression 4x2+8x−5 ? Show all of your work to earn the full points. You can use factor by grouping or box method. If you prefer you can attach a photo of your work using the photo button.
To factor the quadratic expression 4x^2 + 8x - 5, we can use the AC method.
First we multiply the coefficient of the x^2 term (4) by the constant term (-5) which equals -20.
Next, we find two numbers that multiply to -20 and add up to the coefficient of the x term (8). These numbers are 10 and -2.
Now we rewrite the middle term (8x) using the numbers we found:
4x^2 + 10x - 2x - 5
Factor by grouping:
(4x^2 + 10x) + (-2x - 5)
2x(2x + 5) - 1(2x + 5)
Now we have a common binomial factor:
(2x - 1)(2x + 5)
Therefore, the factored form of the quadratic expression 4x^2 + 8x - 5 is (2x - 1)(2x + 5).