Polynomial Review -Lessons 7.1-7.3

All about degrees

100

What degree is this?

X⁴ + X³ - X² + 6

Degree 4

200

Given this table

Find the degree of the polynomial function that models the data.

x  0   1    2    3    4    5 

y  0   3   24  81  192 375

degree 3

300

A degree 7 polynomial with a negative leading coefficient will have at most how many changes in direction (turns)?

6

400

Draw a degree 6 polynomial with a positive leading coefficient 

(should have both ends facing up with 5 turns/peaks)

500

Create a table of 5 values for a polynomial with degree 2 and a common difference of 4

Answers will vary need to check individuals. 

Polynomial math

100

Add the polynomials:

(-3a - 2) + (7a + 5)

4a + 3

200

Subtract the polynomials:

(-5h - 2) - (7h +6)

-12h - 8

300

Multiply the following polynomials

(3r + 5)(4r² + 3r + 3)

12r³+29r²+24r +15

400

Change to general form 

-2(x+5)(3x+2)

-6x^2 - 34x - 20

500

Turn into General Form

−2x⁴+x³+2(x4−x²)

 

x³- 2x²

Let's talk about polynomials

100

If the leading coefficient is positive the right side will go ____________

up or to positive infinity

200

If the leading coefficient is negative and the degree is even what direction will the left hand side go?

down or to negative infinity

300

Given this polynomial what is the y-intercept? Give the answer as a coordinate (x, y)

y=5x⁶−x³+2x²−x−12.

 

(0, -12)

400

Suppose we have a dilation factor of .5 and zeros at -2, -3, and 3.

What is the y-intercept value?

9

500

1/2(x³+8)(x−6)

Tell me everything you can about the polynomial

L.C.

Deg

Turns

End Behavior

Y Intercept

LC = 1/2

Degree = 4

At most 3 turns

Left side up

Right Side Up

Y-int at (0,-24)

What's your form?

100

Which form most easily provides the zeros or roots?

Factored or intercept form

200

Which form easily tells you the y-intercept?

General form?

300

When you're in general form, the terms all are ________________

In descending order by degree/exponents

OR

From biggest to smallest by degree/exponents

400

So far HOW have we written equations of a polynomial when NOT in general form?

What do we need for the OTHER form to write the equation?

The roots or x-intercepts and another point to determine the dilation factor 

500

what is a possible equation to the image?

file:///C:/Users/GWSD/Desktop/Algebra%20II%202022-23/Unit%207/polynomial%20graph.svg

-(X+3)(X+2)(x)(X-2)(x-3)