To factor the polynomial [tex]\(x^2 - 11x + 28\)[/tex], we need to find two numbers that multiply to 28 (the constant term) and add to -11 (the coefficient of the [tex]\(x\)[/tex] term).
Through our calculations, we determine that the two numbers that satisfy these conditions are -4 and -7.
Thus, the polynomial [tex]\(x^2 - 11x + 28\)[/tex] can be factored as:
[tex]\[
(x - 4)(x - 7)
\][/tex]
Now, plugging in the correct values into the provided empty boxes, we get:
[tex]\[
(x - 4)(x - 7)
\][/tex]
Therefore, the complete factored form using the given model is:
[tex]\[
(x - 4)(x - 7)
\][/tex]
Hence, the final answer is:
[tex]\[
(x - 4)(x - 7)
\][/tex]
