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Practice Quiz and Review

You are almost ready to take your lesson quiz.

Before you take a scored quiz for this lesson, try this set of practice questions. Your score on this self-check will be similar to that of your scored quiz. If you do not score well on this self-check, please review this lesson and try again.

(2x + 3)(x2 + 5x + 4)

  1. 2x3 + 13x2 + 23x + 12
  2. 5x5 + 25x3 + 20x
  3. 2x2 + 13x + 35

x2 + 5x + 4
2x + 3
3x2 + 15x + 12
2x3 + 10x2 + 8x
2x3 + 13x2 + 23x + 12

x2 + 5x + 4
2x + 3
3x2 + 15x + 12
2x3 + 10x2 + 8x
2x3 + 13x2 + 23x + 12

x2 + 5x + 4
2x + 3
3x2 + 15x + 12
2x3 + 10x2 + 8x
2x3 + 13x2 + 23x + 12

(x2 + 3x + 2)(x2 + 6)

  1. x3 + 3x2 + 8x + 30
  2. 7x6 + 21x4 + 14x2
  3. x4 + 3x3 + 8x2 + 18x + 12

x2 + 3x + 2
x2 + 6
6x2 + 18x + 12
x4 +3x3 + 2x2
x4 + 3x3 + 8x2 + 18x + 12

x2 + 3x + 2
x2 + 6
6x2 + 18x + 12
x4 +3x3 + 2x2
x4 + 3x3 + 8x2 + 18x + 12

x2 + 3x + 2
x2 + 6
6x2 + 18x + 12
x4 +3x3 + 2x2
x4 + 3x3 + 8x2 + 18x + 12

Summary

Questions answered correctly:

Questions answered incorrectly:


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Vertical Method

The other way you can multiply polynomials is by the Vertical Method. Let's walk through an example of how to multiply polynomials using the Vertical Method.

Suppose you want to multiply the following two polynomials.

(x - 3)(3x2 - 4x + 5)


The first step is to set up this multiplication in a vertical way, lining up terms that have the same degree. Notice how the degree line up in columns:
3x2 - 4x + 5
x - 3
? ? ?
Next multiply each term in the binomial by the terms in the trinomial, lining up the products according to degrees.
3x2 - 4x + 5
x - 3
-9x2 + 12x - 15
3x3 - 4x2 + 5x
Finally, combine like terms. Notice that this method sets this up very nicely for you. Just look down each column.
3x2 - 4x + 5
x - 3
-9x2 + 12x - 15
3x3 - 4x2 + 5x
3x3 - 13x2 + 17x - 15

Vertical Method Practice

Work through the following problems to practice multiplying polynomials using the vertical method. Click on answer to check your work.

Question 1

Multiply: (x + 2)(x2 - 4x + 4)

x2 - 4x + 4
x + 2
2x2 - 8x + 8
x3 - 4x2 + 4x
x3 - 2x2 - 4x + 8

Question 2

Multiply: (2x - 1)(2x2 + x + 3)

2x2 + x + 3
2x - 1
-2x2 - x - 3
4x3 + 2x2 + 6x
4x3 - 0x2 + 5x - 3

= 4x3 + 5x - 3