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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.450R (page 561)

In the following exercises, multiply using (a) the Distributive Property (b) the Vertical Method.
$(x + 1) (x^{2} - 3 x - 21)$ .

Short Answer

Expert verified

(a) using the distributive property is $(x + 1) (x^{2} - 3 x - 21) = x^{3} - 2 x^{2} - 24 x - 21$ .

(b) Using the vertical method $(x + 1) (x^{2} - 3 x - 21) = x^{3} - 2 x^{2} - 24 x - 21$ .

Step by step solution

01

Step 1

Recall the distributive property that $a 路 (b + c) = a 路 b + a 路 c$ .

(a) Use the distributive property to find $(x + 1) (x^{2} - 3 x - 21)$ .

$\begin{array}{rcl} (x + 1) (x^{2} - 3 x - 21) & = & x (x^{2} - 3 x - 21) + 1 (x^{2} - 3 x - 21) \\ = & x (x^{2}) + x (- 3 x) + x (- 21) + x^{2} + 1 (- 3 x) + 1 (- 21) \\ = & x^{3} - 3 x^{2} - 21 x + x^{2} - 3 x - 21 \\ = & x^{3} - 2 x^{2} - 24 x - 21 \end{array}$

So, $(x + 1) (x^{2} - 3 x - 21) = x^{3} - 2 x^{2} - 24 x - 21$ .

02

Step 2

(b) Use the vertical method.

$x^{2} - 3 x - 21 脳 x + 1 x^{2} - 3 x - 21 x^{3} - 3 x^{2} - 21 x x^{3} - 2 x^{2} - 24 x - 21$

So, $(x + 1) (x^{2} - 3 x - 21) = x^{3} - 2 x^{2} - 24 x - 21$ .

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