1. Lesson 1 β 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
βmanyβ) and βnomial (in this case meaning together to get another number, in
βtermβ) . . . so it means βmany termsβ 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. 3π₯!
+ 2π₯!
β π₯ β 7 + π₯!
β 10π₯!
+ 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. 8π₯!
β 3π₯!
β 2π₯ + 9 β 2π₯!
+ 6π₯!
β π₯ + 1
variable is the largest exponent of that Degree =
variable LC =
9. Standard Form (a.k.a. descending order) 3. 2π₯!
+ 3π₯ β 2π₯!
+ 3π₯!
+ π₯ β 4
for writing down a polynomial is to put the Degree =
terms with the highest degree first LC =
i.e. 3π₯!
β 7 + 4π₯!
+ π₯!
the highest degree is 6,
next is 3, then 2, and last the constant
π₯!
+ 4π₯!
+ 3π₯!
β 7
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2. 4. 3π₯ + 1 + π₯!
+ 2π₯!
β 4 β π₯!
β 4π₯!
+ 7π₯ You Try: (work these out on page 60)
Degree = 1. π₯!
+ 2π₯ + 3 π₯!
β 4π₯ + 5
LC = 2. π₯ + 2 3π₯ + 2 2π₯ + 4
III. Multiplying Polynomials 3. 2 π₯!
+ 5π₯ β 1 π₯!
β 2π₯ + 1
Choose Method ~ DISTRIBUTE or BOX
IV. Evaluating Polynomial Functions:
1. 2π₯ β 1 3π₯ + 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. βπ₯!
+ 2π₯ + 4 π₯ + 3 the vertical line test!
Domain: the input values (x-values)
Range: the output values (y-values)
3. π₯!
β 3 3π₯!
β 2π₯ β 4
Evaluate a function: to replace the variables
with a number or expression
4. π₯ β 1 π₯ + 4 π₯ + 3 Evaluate each for the given values:
1. π π₯ = π₯ π 3 π 0 π β2
2. π π₯ = 3π₯!
β 4 π 3 π 0 π β2
5. π₯ β 2 π₯ + 4 π₯ + 2
3. π π₯ = β4π₯!
+ 2π₯
π 3 π 0 π β2
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