3.1 Features
3.2 Add, Subtract, and Multiply
3.3 Polynomial Identites
3.4 Dividing Polynomials
3.5 Zeros of Polynomials
100
What is the degree of the polynomial function:
x3-3x+2
3rd degree
100
Add
(3x3+4x2+1)+(x2-5)
3x3+5x2-4
100
Factor the polynomial
x2-49
(x+7)(x-7)
200
What is the leading coefficient of:
x3-3x+2
1
200
Add
(x4-2x3+5x2-3x+1)+(-x4+2x3-5x2+3x-1)
0
200
Factor the polynomial
x2+12x+36
(x+6)2
300
What are the turning points of the following graph?
(1,4) and (2,0)
300
Subtract
(5x3+4x+8)-(4x3+3x2+2x+10)
x3-3x2+2x-2
300
Factor the polynomial
x3+64
(x+4)(x2-4x+16)
300
Divide: (x² + 5x + 6) ÷ (x + 2)
x + 3
300
Find all zeros of f(x) = x² − 9x + 20, given that (x − 4) is a factor.
Zeros: x = 4 and x = 5
400
What is the domain and range of following graph:
Domain (x-values) (-∞ ,∞)
Range (y-value) (-∞ ,∞)
400
Subtract
(6x³ − 4x² + 9x − 1) − (2x³ + 3x² − 5x + 4)
4x³ − 7x² + 14x − 5
400
Factor the polynomial
x3-125
(x-5)(x2+5x+25)
400
(x³ − 7x + 6) ÷ (x − 2)
x² + 2x − 3
400
Find all zeros of f(x) = 2x³ + x² − 5x + 2, given that (x − 1) is a factor.
Zeros: x = 1, x = ½, x = −2
500
As x->∞ , y -> ? As x->-∞ , y -> ?
As x->∞ , y -> ∞ As x->-∞ , y -> -∞
500
Multiply
(2x + 3)(x² − 4x + 5)
2x³ − 5x² − 2x + 15
500
Factor the polynomial
9x2-36y2
(3x+6y)(3x-6y)
500
(x⁴ − 16) ÷ (x − 2)
x³ + 2x² + 4x + 8
500
Find all zeros of f(x) = x³ − 2x² + 4x − 8, given that (x − 2) is a factor.
Zeros: x = 2, x = 2i, x = −2i