Unit 4 Polynomials

Intro to Polynomials

100

What is the degree and leading coefficient of

f(x)=3(x²-3)(x+4)

degree = 3

Leading coefficient=3

200

What is the degree and leading coefficient of

f(x)=3x²-3^x+6

Not a polynomial

300

Evaluate the function

f(x)= 4x³-3x²+2x-1   at x=2

f(2)=23

400

Describe End Behavior?

What is the behavior of the graph as z approaches positive and negative infinity

500

What is the end behavior of

f(x)=-7x⁵+5x³-12x+12

limf(x) =-infinity when x is going towards + infinity

limf(x)=+infinity when x is going towards - infinity

Add, Subtract and Multiply Polynomials

100

(x²-6x+2) + (5x²-x-8)

6x²-7x-6

200

(8x-3+9x³) - (x³-13x²-4)

8x³+13x²+8x+1

300

(4x²-2+1)(x-2)

4x³-8x²-x+2

400

(x-5)(x+6)(x+2)

x³+3x²-28x-60

500

(y+5)³

y³+15y²+75y+125

Factor and Solve Polynomials

100

2x²-5x-3

(x-3)(2x+1)

200

5x⁵-80x³

5x³(x-4)(x+4)

300

x³+y³

(x+y)(x²-xy+y²)

400

Divide using synthetic division

f(x)=3x³+17x²+21x-11  by g(x)= x+3

3x²+8x-3+ (-2/x+3)

500

27x³+45x²-3x-5=0

x=-5/3,    1/3,   -1/3

Rational Zeros

100

What is the formula for finding the rational zeros?

P  = Factor of a₀

_{___________________}

Q    Factor of a_n

200

List the possible zeros

f(x) = x³-4x²-15x+18

p= +_ 1,2,3,6,9,18

q= +_ 1

300

find all zeros 

f(x)= x³-8x²+5x+14

-1, 2, 7

400

find the zeros of

f(x)= 48x³+4x²-20x+3

x= 1/2

x= -3/4

x=1/6

500

f(x)=5x³+29x²+19x-5

x=-5, -1, 1/5

The Fundamental Theorem of Algebra

100

How many zeros 

f(x)= 3x³+2x²-4x+1

3 zeros

200

How many zeros are there and what are they?

f(x)=(x-3)(x+4)²(x+6)⁴

x=3

x=-4 repeated twice

x=-6 repeated 4 times

300

How many solutions will this equations have

f(x)=(x²-4x+1)³(x+1)²

8 solutions

400

How many rational zeros and what are they

f(x)= x³-9x²+6x-1

x=1

x=1

x=2

x=1/4

500

How many zeros and what are they?

f(x)=2x³+9x²+19x+15

x= - 3/2