Question

Complete the area model representing the polynomial x² - 11x + 28. What is the factored form of the polynomial? Use the model to rewrite the expression.

1) x - 7
2) x² - 7x - 4
3) -4x + 28
4) (x - 7)(x - 4)

Answer 1

The factored form of the polynomial x² - 11x + 28 is (x - 7)(x - 4), using the area model which involves finding two numbers that multiply to 28 and sum to -11, which are -7 and -4.

Step-by-step explanation:

The student is asking to complete the area model for the polynomial x² - 11x + 28 and to find its factored form. To complete the area model, we need to find two numbers that multiply to give the constant term (28) and add up to give the linear coefficient (-11). These two numbers are -7 and -4. We can then represent the area model with four sections: one for x², two for the terms that combine to give -11x (which are -7x and -4x), and one for the constant (+28).

Now, using these sections of the area model, we can rewrite the expression in its factored form. The factored form of x² - 11x + 28 is (x - 7)(x - 4), corresponding to option 4).

Option 1) represents one of the factors, option 2) is a non-factored form of the polynomial with an incorrect coefficient, and option 3) is the result of multiplying -4 with each term of x - 7, but not a factor of the original polynomial by itself.