type the correct answer in each box. use numerals instead of words. complete the area model representing the…

type the correct answer in each box. use numerals instead of words. complete the area model representing the polynomial $x^{2}-11x + 28$. what is the factored form of the polynomial? use the model to rewrite the expression.

type the correct answer in each box. use numerals instead of words. complete the area model representing the polynomial $x^{2}-11x + 28$. what is the factored form of the polynomial? use the model to rewrite the expression.

Answer

Explanation:

Step1: Analyze the polynomial terms

We have the polynomial (x^{2}-11x + 28). In the area - model, when we multiply the terms of the binomials ((x + a)(x + b)=x^{2}+(a + b)x+ab). Here (a + b=-11) and (ab = 28). The two numbers that satisfy these conditions are (-4) and (-7).

Step2: Complete the area - model

The top - right box is (x\times(-7)=-7x). The bottom - left box has (-4x), so the side of the bottom - left box is (-4). The bottom - right box is ((-4)\times(-7) = 28).

Step3: Write the factored form

The factored form of the polynomial (x^{2}-11x + 28) is ((x-4)(x - 7)).

Answer:

Top - right box: (-7x); Bottom - left side: (-4); Bottom - right box: (28); ((x-4)(x - 7))