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
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
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
14

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

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
25

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

**Mini Lecture**

Simplify.

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

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

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

**Mini Lecture**

Multiply.

\(4a^3(3a^2-a+1)\)

\((2a-3)(3a^2-5a+1)\)

\((2a+3)(3a+2)\)

\((x-2)^3\)

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