### Home > INT3 > Chapter 1 > Lesson 1.2.2 > Problem1-91

1-91.

Multiply the expressions.

1. $(x - 1)(x + 1)$

Use an area model to multiply.

In a rectangle, (length)(width) = area. Find the area of each small rectangle inside the area model.

The total area of the rectangle, or $x^2-1$.

1. $2x(x + 1)(x + 1)$

First multiply $2x$ and $(x + 1)$.Then use an area model to multiply that result by $(x + 1)$.

$2x^3+4x^2+2x$

1. $(x - 1)(x + 1)(x - 2)$

$(x^2 - 1)(x - 2)$
Now use an area model.

1. What are the $x$- and $y$-intercepts of the graph of $y = x^3 - 2x^2 - x + 2?$ The factors in part (c) should be useful.

The $x$-intercepts are where $y = 0$.

$0 = x^3 - 2x^2 - x + 2$

The $y$-intercept is where $x = 0$:

$y = 0^3 - 2(0)^2 - 0 + 2$

$0 = (x - 1)(x + 1)(x - 2)$ from part (c).

Using the Zero Product Property: $x - 1 = 0$ or $x + 1 = 0$ or $x - 2 = 0$

$x = 1$, $x = -1$, or $x = 2$