Chapter 4 First Quiz Flashcards
Pattern of Pascal’s Triangle
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1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
How to solve a binomial with Pascal’s Triangle
Write ab
Write a with an exponent of the original exponent number
Write b with a zero exponent
Write a again but with an exponent 1 lower than the first
Write b again but with an exponent 1 higher than the first
** Make sure to multiply the corresponding number in the triangle by ab
What are examples of non-polynomials
y=2^x (exponential)
y= 1/x (a graph that breaks)
y=|x| (absolute value)
y= x^-# (negative power)
y= √x
What is a degree?
The highest power in the equation
What is the leading coefficient?
The first term in the polynomial when it’s written in standard form
(The number in front of the term with the greatest exponent)
How to classify polynomials by degree
0 Constant
1 Linear
2 Quadratic
3 Cubic
4 Quartic
5 Degree #
How to classify polynomials by terms
1 Monomial
2 Binomial
3 Trinomial
4+ Polynomial
Degree: Odd
Leading Coefficient: Positive
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Degree: Odd
Leading Coefficient: Negative
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Degree: Even
Leading Coefficient: Positive
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Degree: Even
Leading Coefficient: Negative
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How do you subtract polynomials?
Distribute the negative and combine like terms
How do you multiply polynomials?
Multiply every term on both sides
True or False?
When combining like terms using Pascal’s Triangle, you square the number and also add the exponent in the final answer
True
How to divide polynomials using synthetic division
- Identify all coefficients
- Identify k; x+# (WILL BE OPPOSITE x-#)
- Set up chart
- Drop the first coefficient
- Multiply k and first coefficient
- Add 2nd coefficient and new number (k and first coefficient multiplied)
- Repeat
True or false
You can use synthetic division for all numbers
False
You can only use synthetic division when dividing by a binomial
What is a placeholder?
A 0x number to fill in for a coefficient that isn’t there
REMEMBER TO USE THEM
***Divide like normal
How to divide a polynomial by a polynomial
- Put the number on the left divided by the number on the right
- Find what would multiply by the first term on the left to equal the first term in the middle
- Multiply that by every term on the left and subtract
- Drop down every term and repeat until there are no exponents left
True or false the number on the left is the one under the division thing.
True
The number on the left is the one under the division thing
Thing to remember
If the two numbers have the same amount of terms, you will have a single number as an answer.
What has to be even or odd when finding end behavior of a function?
The degree
What has to be negative or positive when finding the end behavior of a function?
The leading coefficient
