Question

1. make sense and persevere the area of a rectangle is given. identify the missing terms in the length and width.

(x + _)
x^{2}+11x + 28 (_ + 4)

1. use structure the table shows the product when multiplying two binomials. what is the relationship between the numbers in the factors and the terms in the product?

binomials products
(x + 3)(x + 4) x^{2}+7x + 12
(x + 2)(x - 5) x^{2}-3x - 10
(x - 3)(x - 5) x^{2}-8x + 15

Explanation:

Step1: Factor the quadratic expression

We know that for a quadratic expression \(ax^{2}+bx + c\) (in our case \(a = 1\), \(b=11\), \(c = 28\)), we need to find two numbers that multiply to \(ac=28\) and add up to \(b = 11\). The numbers are \(4\) and \(7\) since \(4\times7=28\) and \(4 + 7=11\). So \(x^{2}+11x + 28=(x + 4)(x+7)\).

Answer:

The missing terms are \(7\) and \(x\) (from left - to - right).