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

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Example 1

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

Example 2

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

Example 3

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

Example 4

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

Example 5

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

Example 6

Add \(5x^2-4x+2\) and \(3x^2+9x-6\)

Example 7

Find the sum of \(-8x^3+7x^2-6x\) and \(10x^3+3x^2-2x-6\)

Example 8

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

Example 9

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

Example 10

Find the value of \(5x^3-3x^2+4x-5\) when \(x\) is \(2\)

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 \(P(100)\).

Example 12

Find the product of \(4x^3\) and \(5x^2-3x+1\)

Example 13

Multiply \(2x-3\) and \(x+5\)

Example 14

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

Example 15

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

Example 16

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

Example 17

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

Example 18

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

Example 19

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

Example 20

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

Example 21

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

Example 22

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

Example 23

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

Example 24

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

Example 25

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

Example 26

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

Example 27

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

Example 28

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

Example 29

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

Example 30

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

Mini Lecture
Simplify.

  1. \(2x^2-3x+10x-15\)

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

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

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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