Algebra 2 Study Guide - Polynomials
1. How to classify a polynomial - Degree and Term (Example: Cubic Trinomial)
• Degree: Linear, Quadratic, Cubic, and Quartic
• Term: Monomial, Binomial, Trinomial, and Polynomial
2. Standard Form: 5x4 + 4x3 + 3x2 + 2x + 1
3. What is the relationship between the degree of the polynomial and the number of roots?
4. What do the two parent graphs of polynomials look like?
5. Sketch the graph
a. 3x3 + 2x + 1
b. –x6 + x4 + 2
6. End behaviors: Give the end behaviors of the three graphs above
7. Find the sum or difference:
a. (4x3 – 3x2 + x – 4) + (7x2 – x + 1)
b. (x4 + 6x3 – x – 8) – (4x4 + 5x3 – 2x – 7)
c. –x5 + x4 + 3x
8. Find the product:
a. (x + 3)(x2 + 3x – 7)
b. (x + 2)(x – 3)(x – 6)
9. Find the quotient:
a. Is (x + 2) a factor of (x3 + 5x2 – 5)
b. Is (2x + 1) a factor of (2x3 + 3x2 – 3x – 2)
c. Is 2 a factor of (x3 + 3x2 – 4x – 13)
Factoring:
a. 9x2 – 24x + 16
b. 2x3 – 2x2 – 40x
c. x3 – 4x2 – 7x + 28
d. x5 – 12x3 + 27x
e. 36x2 - 25
f. 27x3 – 1
g. 64x3 + 1
h. x4 - 81
i. 2x5 – 16x3 + 30x
j. x3 - 3x2 – 10x
Remember How to FACTOR!
Easy Button
Crack the Egg
a2 – b2 = (a – b)(a+b)
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 - ab + b2)
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2