Question

1. what are the advantages of using the area model for polynomial multiplication?

a. simplicity
b. none
c. visualization
d. speed

1. what is the final simplified form of the product $(x - 4)(x + 5)$?

a. $x^2 + 5x - 4x$
b. $x^2 - x - 20$
c. $x^2 + x - 20$
d. $x^2 - 20$

1. what does $(x + 1.5)(x - 2.5)$ equal?

a. $x^2 - x + 3.75$
b. $x^2 + x - 3.75$
c. $x^2 + 3.75$
d. $x^2 - x - 3.75$

Explanation:

Step1: Answer first question

The area model for polynomial multiplication uses rectangles to represent the product, making the process visual.

Step2: Expand second product via FOIL

First: $x \times x = x^2$, Outer: $x \times 5 = 5x$, Inner: $-4 \times x = -4x$, Last: $-4 \times 5 = -20$. Combine terms: $x^2 +5x-4x-20 = x^2+x-20$.

Step3: Expand third product via FOIL

First: $x \times x = x^2$, Outer: $x \times (-2.5) = -2.5x$, Inner: $1.5 \times x = 1.5x$, Last: $1.5 \times (-2.5) = -3.75$. Combine terms: $x^2 -2.5x+1.5x-3.75 = x^2 -x-3.75$.

Answer:

1. c. Visualization
2. c. $x^2 + x - 20$
3. d. $x^2 - x - 3.75$