Question

Determine the missing factor for 5x2 + 6x - 8 = (______)(x + 2)

Answer 1

To find the missing factor in the equation
`5x^2 + 6x - 8 = (---------)(x + 2)`, factor the quadratic to get (5x - 4)(x + 2); hence, the missing factor is (5x - 4).

Step-by-step explanation:

The student is asked to determine the missing factor in the quadratic equation
`5x^2 + 6x - 8 = (--------)(x + 2)`. To find the missing factor, we can attempt to factor the quadratic expression on the left-hand side.

Begin by looking for two numbers that multiply to give the product of the coefficient of
`x^2 (5)` and the constant term (-8), which is -40, and add to give the coefficient of x (6).

These numbers are 10 and -4. Therefore, the quadratic expression can be factored as (5x - 4)(x + 2).

So the missing factor that would be multiplied by (x + 2) to get
`5x^2 + 6x - 8` is (5x - 4).