#5. Factor the trinomial.

Question

Type your answers to each problem in the table below. The order of the factors doesn't matter, but use parentheses around each one! x^2 - 11x + 28

Answer 1

To factor the trinomial \( x^2 - 11x + 28 \), we look for two numbers that multiply to \( 28 \) (the constant term) and add to \( -11 \) (the coefficient of \( x \)).

The numbers that satisfy these conditions are \( -7 \) and \( -4 \) because:

• \((-7) + (-4) = -11\)
• \((-7) \times (-4) = 28\)

Thus, we can factor the trinomial as:

\[ (x - 7)(x - 4) \]

So the answer is: \((x - 7)(x - 4)\)