Notes for student NB to save time!! I created these notes for students in CCMath 2, the lesson is a review of CCMath 1 content.

1. Lesson 1 – Operations with Polynomials 10. Polynomial Function ~ relates an input to
I. Vocabulary an output, three main parts
1. Constant ~ is a number (on its own)
2. Term ~ is either a single number or a the input
variable, or numbers & variables multiplied the relationship
together. . . terms are separated by +/- the output
3. Polynomial~ comes from poly- (meaning 11. Factors ~ are numbers you can multiply
“many”) and –nomial (in this case meaning together to get another number, in
“term”) . . . so it means “many terms” they algebra factors are what you can
can have constants, variables, and can multiply together to get an
exponents but NEVER division by a variable.
4. Monomial ~ is a polynomial with 1 term II. Add/Subtract Polynomials
5. Binomial ~ is a polynomial with 2 terms *COMBINE LIKE TERMS!
6. Trinomial ~ is a polynomial with 3 terms 1. 3𝑥!
+ 2𝑥!
− 𝑥 − 7 + 𝑥!
− 10𝑥!
+ 8
7. Leading Coefficient ~ is the coefficient of Degree =
the first term of a polynomial LC =
8. Degree ~ (of a polynomial) with only one 2. 8𝑥!
− 3𝑥!
− 2𝑥 + 9 − 2𝑥!
+ 6𝑥!
− 𝑥 + 1
variable is the largest exponent of that Degree =
variable LC =
9. Standard Form (a.k.a. descending order) 3. 2𝑥!
+ 3𝑥 − 2𝑥!
+ 3𝑥!
+ 𝑥 − 4
for writing down a polynomial is to put the Degree =
terms with the highest degree first LC =
i.e. 3𝑥!
− 7 + 4𝑥!
+ 𝑥!
the highest degree is 6,
next is 3, then 2, and last the constant
𝑥!
+ 4𝑥!
+ 3𝑥!
− 7
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2. 4. 3𝑥 + 1 + 𝑥!
+ 2𝑥!
− 4 − 𝑥!
− 4𝑥!
+ 7𝑥 You Try: (work these out on page 60)
Degree = 1. 𝑥!
+ 2𝑥 + 3 𝑥!
− 4𝑥 + 5
LC = 2. 𝑥 + 2 3𝑥 + 2 2𝑥 + 4
III. Multiplying Polynomials 3. 2 𝑥!
+ 5𝑥 − 1 𝑥!
− 2𝑥 + 1
Choose Method ~ DISTRIBUTE or BOX
IV. Evaluating Polynomial Functions:
1. 2𝑥 − 1 3𝑥 + 4
Function: a relation for which each value
from the domain (input) is paired with exactly
one value in the range (output). *must pass
2. −𝑥!
+ 2𝑥 + 4 𝑥 + 3 the vertical line test!
Domain: the input values (x-values)
Range: the output values (y-values)
3. 𝑥!
− 3 3𝑥!
− 2𝑥 − 4
Evaluate a function: to replace the variables
with a number or expression
4. 𝑥 − 1 𝑥 + 4 𝑥 + 3 Evaluate each for the given values:
1. 𝑓 𝑥 = 𝑥 𝑓 3 𝑓 0 𝑓 −2
2. 𝑓 𝑥 = 3𝑥!
− 4 𝑓 3 𝑓 0 𝑓 −2
5. 𝑥 − 2 𝑥 + 4 𝑥 + 2
3. 𝑓 𝑥 = −4𝑥!
+ 2𝑥
𝑓 3 𝑓 0 𝑓 −2
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3. 4. 𝑔 𝑥 = 5𝑥!
+ 4𝑥!
− 5 4. 𝑔 𝑥 = 5𝑥!
+ 4𝑥!
− 5
3 𝑔 2 𝑔 2 + 5 −2𝑔 2 − 7 3 𝑔 2 𝑔 2 + 5 −2𝑔 2 − 7
5. 𝑓 𝑥 = 4𝑥 + 3 𝑓 2𝑦 5. 𝑓 𝑥 = 4𝑥 + 3 𝑓 2𝑦
6. 𝑓 𝑥 = 3𝑥 − 7 𝑓 𝑥 − 4 6. 𝑓 𝑥 = 3𝑥 − 7 𝑓 𝑥 − 4
7. 𝑓 𝑥 = 3𝑥!
− 2𝑥 + 5 𝑓 𝑥 + 2 7. 𝑓 𝑥 = 3𝑥!
− 2𝑥 + 5 𝑓 𝑥 + 2
8. 𝑓 𝑥 = −𝑥!
+ 6𝑥 − 2 𝑓 −4𝑥 8. 𝑓 𝑥 = −𝑥!
+ 6𝑥 − 2 𝑓 −4𝑥
9. 𝑓 𝑥 = 𝑥!
− 9𝑥 + 8 𝑓 𝑥 − 1 9. 𝑓 𝑥 = 𝑥!
− 9𝑥 + 8 𝑓 𝑥 − 1
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Page Page 61
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