The problem is to factor the quadratic polynomial $x^2 - 6x + 8$. We need to find two binomials that multiply to give the given polynomial.

1. Problem Description

The problem is to factor the quadratic polynomial $x^2 - 6x + 8$. We need to find two binomials that multiply to give the given polynomial.

2. Solution Steps

We need to find two numbers that multiply to 8 and add to -

6. The factors of 8 are:

1 and 8

2 and 4

-1 and -8

-2 and -4

We can see that -2 and -4 add up to -6 and multiply to

8.

Therefore, we can write the factored form as $(x - 2)(x - 4)$.

We can verify this by expanding:

$(x - 2)(x - 4) = x(x - 4) - 2(x - 4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8$.

3. Final Answer

$(x-2)(x-4)$