Which of the following is a solution to the equation x^2 - 2x - 8 = 0? — SAT

Which of the following is a solution to the equation $x^2 - 2x - 8 = 0$ ?

The correct solution is 4.

To find the solutions to the equation

x^2 - 2x - 8 = 0

, we factor the quadratic expression on the left side of the equation. We need two numbers that multiply to

-8

and add to

-2

. These numbers are

-4

and

2

. Thus, the equation can be rewritten in factored form as

(x - 4)(x + 2) = 0

. Setting each factor to zero yields the solutions

x = 4

and

x = -2

. Among the given options,

4

is the only correct solution.

Factor the quadratic expression

x^2 - 2x - 8

The expression factors into

(x - 4)(x + 2)

We look for two numbers that multiply to the constant term

-8

and add to the linear coefficient

-2

. These numbers are

-4

and

2

Set each factor equal to zero to solve for

x

x - 4 = 0

x + 2 = 0

, which gives

x = 4

x = -2

By the zero product property, if the product of two factors is zero, then at least one of the factors must be zero.

Identify the solution that appears in the options.

x = 4

is a solution.

Checking the given options,

4

is listed while

-2

is not.

Solving quadratic equations by factoring

Question