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Factoring Bootcamp
Review: Sums, Differences, and Products of Polynomials

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Welcome to Lesson 1

Example 1

Identify $$6x^2+2x-1$$ as a monomial, binomial, or trinomial if possible and give the degree.

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Cynthia
(Spanish)

Example 2

Identify $$5x-3$$ as a monomial, binomial, or trinomial if possible and give the degree.

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Julieta
(Spanish)

Example 3

Identify $$7x^6-5x^3+2x-4$$ as a monomial, binomial, or trinomial if possible and give the degree.

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Cynthia
(Spanish)

Example 4

Identify $$-7x^4$$ as a monomial, binomial, or trinomial if possible and give the degree.

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Julieta
(Spanish)

Example 5

Identify $$15$$ as a monomial, binomial, or trinomial if possible and give the degree.

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Cynthia
(Spanish)

Example 6

Add $$5x^2-4x+2$$ and $$3x^2+9x-6$$

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Edwin
(Spanish)

Example 7

Find the sum of $$-8x^3+7x^2-6x$$ and $$10x^3+3x^2-2x-6$$

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Julieta
(Spanish)

Example 8

Subtract $$\left(9x^2-3x+5\right)-\left(4x^2+2x-3\right)$$

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David
(Spanish)

Example 9

Simplify $$4x-3[2-(3x+4)]$$

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Julieta
(Spanish)

Example 10

Find the value of $$5x^3-3x^2+4x-5$$ when $$x$$ is $$2$$

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Cynthia
(Spanish)

Example 11

A company produces and sells copies of an accounting program for home computers. The total weekly cost (in dollars) to produce $$x$$ copies of the program is $$C(x)=8x+500$$. Find its weekly profit if the total revenue obtained from selling all $$x$$ programs is $$R(x)=35x-0.1x^2$$. How much profit will the company make if it produces and sells $$100$$ programs a week? That is, find $$P(100)$$.

Julieta
(Spanish)

Example 12

Find the product of $$4x^3$$ and $$5x^2-3x+1$$

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Julieta
(Spanish)

Example 13

Multiply $$2x-3$$ and $$x+5$$

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Edwin
(Spanish)

Example 14

Multiply $$(2x-3y)$$ and $$\left(3x^2-xy+4y^2\right)$$ vertically.

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Cynthia
(Spanish)

Example 15

Multiply: $$(4a-5b)(3a+2b)$$

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Edwin
(Spanish)

Example 16

Multiply: $$(3-2t)(4+7t)$$

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Julieta
(Spanish)

Example 17

Multiply $$\left(2x+\displaystyle\frac{1}{2}\right)\left(4x-\displaystyle\frac{1}{2}\right)$$

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Edwin
(Spanish)

Example 18

Multiply $$\left(a^5+3\right)\left(a^5-7\right)$$

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Julieta
(Spanish)

Example 19

Multiply: $$(2x+3)(5y-4)$$

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Edwin
(Spanish)

Example 20

Find $$(4x-6)^2$$

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Julieta
(Spanish)

Example 21

Expand $$(x+7)^2$$

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Edwin
(Spanish)

Example 22

Expand $$(3t-5)^2$$

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Julieta
(Spanish)

Example 23

Expand $$(4x+2y)^2$$

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Edwin
(Spanish)

Example 24

Expand $$\left(5-a^3\right)^2$$

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Julieta
(Spanish)

Example 25

Multiply: $$\left(x+\dfrac{1}{3}\right)^2$$

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Cynthia
(Spanish)

Example 26

Multiply $$(3x-5)$$ and $$(3x+5)$$

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Edwin
(Spanish)

Example 27

Multiply: $$(x-5)(x+5)$$

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Julieta
(Spanish)

Example 28

Multiply: $$(2a-3)(2a+3)$$

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Edwin
(Spanish)

Example 29

Multiply $$\left(x^2+4\right)\left(x^2-4\right)$$

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Julieta
(Spanish)

Example 30

Multiply $$\left(x^3-2a\right)\left(x^3+2a\right)$$

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Edwin
(Spanish)

Mini Lecture
Simplify.

1. $$2x^2-3x+10x-15$$

2. $$\left(5x^2+6x+1\right)-\left(4x^2+7x-2\right)$$

3. $$4x-5\left[3-(x-4)\right]$$

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Mini Lecture
Multiply.

1. $$4a^3(3a^2-a+1)$$

2. $$(2a-3)(3a^2-5a+1)$$

3. $$(2a+3)(3a+2)$$

4. $$(x-2)^3$$

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