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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.206 (page 537)

In the following exercises, multiply using a) the Distributive Property; b) the Vertical Method
$(x + 5) (x^{2} + 4 x + 3)$

Short Answer

Expert verified

The product of the given polynomials is $x^{3} + 9 x^{2} + 23 x + 15$

Step by step solution

01

Step 1. Given Information

The given polynomials are $(x + 5) (x^{2} + 4 x + 3)$

The product is to be determined using a) the Distributive Property; b) the Vertical Method

02

Part (a) Step 1. Using distributive property

According to distributive property:

$(x + 5) (x^{2} + 4 x + 3) = x (x^{2} + 4 x + 3) + 5 (x^{2} + 4 x + 3) (x + 5) (x^{2} + 4 x + 3) = x^{3} + 4 x^{2} + 3 x + 5 x^{2} + 20 x + 15 (x + 5) (x^{2} + 4 x + 3) = x^{3} + 9 x^{2} + 23 x + 15$

03

Part (a) Step 2. Conclusion

The product of the polynomials is $x^{3} + 9 x^{2} + 23 x + 15$

04

Part (b) Step 1. Using Vertical Method

Multiplying using vertical method:

$\begin{array}{rrr} x^{2} + & 4 x + & 3 \\ 脳 & x + & 5 \\ 5 x^{2} + & 20 x + & 15 \\ x^{3} + 4 x^{2} + & 3 x \\ x^{3} + 9 x^{2} + & 23 x + & 15 \end{array}$

05

Part (b) Step 2. Conclusion

The product of the polynomials is $x^{3} + 9 x^{2} + 23 x + 15$

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