Unit 5 Are you Ready?

Unit 5 Are you Ready?

Polynomial Functions

Polynomials

expressions of whole number powers with one or more variables that are multiplied by coefficients

In Unit 5, we will

• multiply polynomials

• divide polynomials

• factor polynomials

• solve/find roots of polynomials

• graph/transform polynomials

• Do these topcis seem familiar??

Multiple Choice

What is the y-value of the highest point of a function?

• coefficient

• maximum

• x-intercept

Multiple Choice

What is the numerical factor in a term?

• coefficient

• like terms

• x-intercept

Multiple Choice

What is the value of a variable that makes the equation true?

• x-intercept

• terms in the equation that have the same variables

• root of an equation

Multiple Choice

What are terms that contain the same variables raised to the same powers?

• x-intercepts

• like terms

• root of an equation

Multiple Choice

What is the x-coordinate of a point where a graph intercepts the x-axis?

• like terms

• x-intercept

• the horizontal number line that divides the coordinate plane

Working with Exponents

Raising of powers is something you've done since Algebra 1. You should be able to evaluate expressions with raised powers during this point in your math coursework. Get your calculator!

Fill in the Blank

Simplify

$$6^4$$  

Fill in the Blank

Simplify

$$-5^4$$  

Fill in the Blank

Simplify

$$\left(-1\right)^5$$  

Fill in the Blank

Simplify

$$\left(-\frac{2}{3}\right)^2$$  

Evaluate

When you evaluate, you solve with the given number

Fill in the Blank

Evaluate

$$x^{4\ }-5x^2-6x-8$$  for x = 3

Fill in the Blank

Evaluate

$$2x^{3\ }-3x^2-29x-30$$  for x = -2

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Evaluate

$$2x^3-x^2-8x\ +4\ for\ x\ =\frac{1}{2}$$  

Fill in the Blank

Evaluate

$$3x^4+5x^3+6x^2\ +4x-1\ for\ x\ =-1$$  

Multiplying/Dividing Monomials

• Remember that when you multiply variables with exponents, you need to multiply the coefficients and add the exponents

• Remember when you divide variables with exponents, you divide the coefficients and subtract the exponents

• Ex: 8x³ / 2x = 4x²

Multiple Choice

$$2x^3y\ \cdot\ 4x^2$$  =

• $$8x^3y^2$$  

• $$8x^5y$$  

• $$6x^5y^2$$  

• $$6x^5y$$  

Multiple Choice

$$-5a^2b\ \cdot\ ab^4$$  

• $$-5a^3b^5$$  

• $$5a^3b^5$$  

• $$-10a^3b^5$$  

• $$-4a^5b^4$$  

Multiple Choice

$$\frac{-7t^4}{3t^2}$$  

• $$-7t^2$$  

• $$\frac{-3t^2}{7}$$  

• $$\frac{-7}{3}t$$  

• $$\frac{-7}{3}t^2$$  

Multiple Choice

$$\frac{3p^3q^2r}{12pr^4}$$  

• $$\frac{4p^2q^2}{pq}$$  

• $$\frac{4r}{pq}$$  

• $$\frac{p^2q^2}{4r^2}$$  

• $$\frac{p^2q^2}{4r^3}$$  

Multiple Choice

What is the surface area of a cube with side 4 cm

• 16

• 64

• 96

• 128

Multiple Choice

What is the surface area of a rectangular prism with height 3 ft, width 1.5 ft, and length 8 ft?

• 36

• 81

• 108

• 72

Fill in the Blank

What is the volume of a rectangular prism height 1 in, width 6 in, and length 2/3 in? _______ in³

Fill in the Blank

What is the volume of a rectangular prism with height 5 cm and a square base with side length 2 cm? ______ cm³