Question

Which expression is equal to x−7x2+8−x2−x+6x2+8 ?

Responses

x2+2x−132x2+16


−x2+2x−13x2+8


x2+2x−13x2+8


−x2+2x−132x2+16

Answer 1

x2+2x−132x2+16

Explanation:

First, let's simplify the expression by combining like terms:

x - 7x^2 + 8 - x^2 - x + 6x^2 + 8

= -7x^2 + 5x^2 - x^2 + x + 16

= -x^2 + 2x + 16

Now we need to factor the quadratic expression -x^2 + 2x + 16. We can use the quadratic formula or complete the square to find the roots, but it turns out that the expression doesn't factor nicely. However, we can rewrite it as -(x^2 - 2x - 16) and then use the quadratic formula to find the roots of the expression inside the parentheses:

x = (-(-2) ± sqrt((-2)^2 - 4(-16)))/(2(1))

x = (2 ± sqrt(68))/2

x = 1 ± 2sqrt(17)/2

x = 1 ± sqrt(17)

So we have:

-x^2 + 2x + 16 = -(x - (1 + sqrt(17)))(x - (1 - sqrt(17)))

Therefore, the expression is equal to -x^2 + 2x + 16, which corresponds to the option:

x^2 + 2x - 13 / 2x^2 + 16