Introduction to Polynomials

Introduction to Polynomials Review

What is a Polynomial Expression?

• Any expression that includes variables as bases and positive integers as exponents

• Example:  $4x^2+8x+1$  

Multiple Choice

Which of the following is a polynomial expression?

• $$2^x+5^x$$

• $$8x^3+7x+2$$

• $$4x^2+\frac{1}{x}$$

• $$\frac{3}{x^2}+\frac{5}{x}$$

Multiple Choice

Which of the following is not a polynomial expression?

• $$x^2-3x+7$$

• $$6x$$

• $$11x^7+5x^2$$

• $$\frac{5}{x^2}$$

What is Standard Form for Polynomials?

• The powers of the polynomial are in descending order

• Example:  $9x^4-x^2+2x+1$  

Multiple Choice

Write the following polynomial expression in standard form:

$$11x^2-9x^4+3x^3+7$$  

• $$9x^4+11x^2+3x^3+7$$  

• $$7+11x^2+3x^3-9x^4$$  

• $$-9x^4+3x^3+11x^2+7$$

• $$-9x^4+11x^2+3x^3+7$$  

Multiple Choice

True or False:
The following polynomial is in standard form

$$2x^5+8x^3+3x^2+7$$  

• True

• False

Adding Polynomials

• Add the like terms together

• Example:  $3x^2+5x^2+2x=8x^2+2x$  

Multiple Choice

Find the sum of the following polynomials:

$$x^3+4x^2-8x+3+x^3-x+1$$  

• $$2x^3+4x^2-7x+3$$  

• $$x^5+4x^2-8x+4$$  

• $$2x^3+4x^2-9x+4$$  

• $$x^3+4x^2-9x+4$$  

Subtracting Polynomials

• Distribute the negative sign into the second polynomial, then combine like terms

• Example:  $\left(5x^2+3x\right)-\left(3x^2+2x\right)$  

•  $5x^2+3x-3x^2-2x$  

•  $2x^2+x$  

Multiple Choice

Find the difference of the following polynomials.

$$\left(4x^2+6x-3\right)-\left(3x^2+2x+4\right)$$  

• $$x^2+4x-7$$  

• $$7x^2+8x+1$$  

• $$x^2+4x+1$$  

• $$7x^2+4x-7$$  

Multiplying Polynomials

• Use the Distributive Method

• Draw your arrows!

Multiple Choice

Find the product of the following polynomials.

$$x^2\left(4x+3\right)$$  

• $$4x^3+3x^2$$  

• $$4x+3x^2$$  

• $$4x^3+3$$  

• $$4x+3$$  

Multiple Choice

Find the product of the following polynomials.

$$\left(x+2\right)\left(x-6\right)$$  

• $$x^2-8x-12$$  

• $$x^2-4x-12$$  

• $$x^2-4x+12$$  

• $$x^2+4x+12$$  

Great Job!

Let's move onto the second part of our review!