Polynomials Monomials one term Can be one of the following ...€¦ · 1. Number 1, 2, 3, ... 2....
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Polynomials Monomials one term Can be one of the following: 1. Number 1, 2, 3, ... 2. Variable x, y, z, ... 3. Number & Variable(s) 2x, 3x 2 , 4xy, 5x 2 y 3 *multiplying the number and variable(s) together Prefix Name # of Terms Mono Monomial 1 term Bi Binomial 2 terms Tri Trinomial 3 terms Poly Polynomial 4 or more terms *Polynomial is the general term.
Transcript of Polynomials Monomials one term Can be one of the following ...€¦ · 1. Number 1, 2, 3, ... 2....
PolynomialsMonomials one term
Can be one of the following:
1. Number 1, 2, 3, ...
2. Variable x, y, z, ...
3. Number & Variable(s) 2x, 3x2, 4xy, 5x2y3
*multiplying the number and variable(s) together
Prefix Name # of TermsMono Monomial 1 term
Bi Binomial 2 terms
Tri Trinomial 3 terms
Poly Polynomial 4 or more terms
*Polynomial is the general term.
Ordering Polynomials Order polynomials by the variables, NOT by the coefficients (numbers)
Variables are arranged in order from A to Z
4xzy 4xyz
6c2ab3 6ab3c2
Order terms by alphabetical order.
If there is a letter that is the same, order it by degree of the exponent before moving on to the next letter.
Put in correct order.4xy + 3x + 2y
Put in correct order.5ac + 2a + 4b + 3ab
Degree highest exponent of the variable
Highest exponent goes first in ordering.Put in correct order.
4x + 5x2 + 6 + 2x3
Put in correct order.2xy + 5x2y + 3y3 + 4x
Put in correct order.2xy2 + 3x2y + 4x3y + 4 + 2x2y2
Operations with PolynomialsAddition:
(x + 2) + (x 3)"find the sum of"
Subtraction:(x + 2) (x 3)
"find the difference of"
Multiplication:(x + 2)(x 3)
"find the product of"
This is the "easy" part of theunit, but this is the #1 thing that students mess up on the assessment because they forget how to do it after we start doing the "hard" stuff.
Adding Polynomials***Only can add (or combine) LIKE TERMS***
Q: What is a like term?A: Terms having the same variable(s) with the same exponent(s)
3x2 & 4x 3x2 & 2x2 4x2yz & 6xy2z
If NOT like terms, then NOT able to combine
To add polynomials:
Add the coefficients (#s) of the like terms.*Leave the variables/exponents the way they are
Find the sum.
4x + 3y + 8y + 2x
Find the sum.
(2x + 3y) + (5x 8y)
Find the sum.
(3x2 + 5x 2y) + (6x2 + 3y)
Find the sum.
(x3 + 5x2 + 9x 6) + (5x3 8x + 1)
What is the sum of 2x + 3y and x 5y?
Perimeter is the distance around the outside.
4x 8
y + 11
2x + 3
Write a polynomial that represents the perimeter of the figure shown below.
x2 2
x + 3
3x 4
x2 2x + 1
A rectangle has 2 sets of sides with the same length.
Find perimeter (P) using the formula, 2L + 2W = P4x + 3y + 5
2x + 6
Subtracting Polynomials***Only can subtract (or combine) LIKE TERMS***
***Must distribute the "ghosty 1" FIRST to every term in the parenthesis that it is next to before combining like terms***
(x + 2) (4x2 2x + 1)
Find the difference.
(x2 4x) (3x2 + 4x)
Find the difference.
(3x2 8x + 6) (2x2 + 3x 5)
Find the difference.
(5x3 + 3x2 + 1) (2x3 x2 + 3)
What is the difference when x2 3x 1 is subtracted from 3x2 + 5x 6?
What is the difference when 6x3 8 is subtracted from 3x2 + 4x + 3?
What is the length of the missing side if the perimeter of the figure is 13x + 2?
?
What is the width of the rectangle if the length is 4x + 8 and the perimeter is 12x + 22?
4x + 8 2(4x + 8) + 2(width) = 12x + 22
(8x + 16) + 2(width) = 12x + 22
2(width) = (12x + 22) (8x + 16)
2(width) = 4x + 6 = 2x + 3 2 2
