Polynomials Review

Vocabulary

100

How many terms are in a trinomial?

Three

200

Name the polynomial: 2x⁴+9x³-5x²+6

Be sure to include the degree and number of terms

quartic polynomial with 4 terms

300

What does it mean to write a polynomial in standard form?

reorder the terms such that the exponents are in descending order.

400

Write an example of a quadratic trinomial.

I will check

500

Like terms need to have...(two things!!)

1. Same variables

2. Same exponents

End Behavior and Multiplicity

100

What is the end behavior of the polynomial:

 p(x) = -3x²+6x-4

down, down

200

What does the multiplicity help determine on the graph?

Behavior at the x-intercepts.

bounce: multiplicity is even

cross: multiplicity is odd

300

What aspects of the polynomial do we need to analyze to determine end behavior?

Leading coefficient and degree

400

A polynomial with a negative leading coefficient and odd degree will have an end behavior of...

up, down

500

Sketch the following polynomial:

-x(x+2)³(x-1)²

I will check

Solving Polynomialsby Factoring

100

Solve the following by factoring:

x² + 7x + 12 = 0

(x+4)(x+3)=0

x = -4 x = -3

200

Solve:

(x-2)(x+3)(x²+4)=0

x=2

x= -3

x=2i

x=-2i

300

Solve by factoring:

2x³+10x²+12x=0

2x(x²+5x+6)=0

2x(x+3)(x+2)=0

x=0, x=-3, x=-2

400

Solve by factoring:

x³-5x²-2x+10=0

(x² - 2)(x-5)=0

x= +/- sqrt 2

x= 5

500

Solve by Factoring:

16x³-28x²+4x-7=0

(4x²+1)(4x-7)=0

x= 7/4

x= +/- 0.5i

Synthetic division

100

What is the name of the other method of division we learned?

long division

200

What is the divisor of the following polynomial

(x³+7x²+12x-3) divided by (x+5)

(x+5)

300

What is the remainder of:

(x³+7x²+12x-3) divided by (x+5)

Remainder = -13

400

What is the quotient of:

(x³+6x²+10x+3) divided by (x+3)

x²+3x+1

500

What is the name of the theorem that allows you to check your synthetic division?

Remainder Theorem

Fundamental Theorem of Algebra

100

How do we determine the number solutions of a polynomial? 

degree of the polynomial (highest exponent)

200

How many complex solutions does the polynomial have?

3x³+4x⁵+6x³+20

5 complex solutions

300

If x= -3 is an x-intercept of x³+3x²+9x+27, what are the remaining solutions?

x= 3i

x= -3i

400

If x=3 is a solution of the polynomial x³+5x²+x-75, what are the complex zeros?

x = -4 + 3i

x= -4 - 3i

500

The polynomial x⁴+4x³+7x²+16x+12 has x-intercepts at x= -3 and x= -1. Find the other solutions

x = 2i

x= -2i