Polynomials. Unit 2: Algebra Investigation MM1A2c: Add, subtract, multiply, and divide polynomials....

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Transcript of Polynomials. Unit 2: Algebra Investigation MM1A2c: Add, subtract, multiply, and divide polynomials....
Polynomials
Unit 2: Algebra Investigation
MM1A2c: Add, subtract, multiply, and divide polynomials.
Essential Question:
How do you add and subtract polynomials?
What does each prefix mean?
mono
one
bi
two
tri
three
What about the prefix: poly?MANY
A polynomial is a monomial or a sum or difference of monomials. Each monomial called a term.
Important Note!An expression is not a polynomial if there is a variable
in the denominator.
Different Types of Polynomials
Monomial: number (1, 2, 3, …), variable (a, b, c, …) or the product of a number and one or more variable (2x, 4xyz,…)
Binomial: Two terms (2x + 4y, 3xz + 5)
Trinomial: Three terms (4a + 2ab + 7b)
State whether each expression is a polynomial. If it is, identify it.
1) 7y  3x + 4
trinomial
2) 10x3yz2
monomial
3)
not a polynomial2
57
2y
y
Degree of a Monomial
• The sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is 0.
Ex. 4x3y2
The degree of the monomial is “5”
Find the degree of each monomial.
1) 5x2
2
2) 4a4b3c
8
3) 3
0
Degree of a Polynomial
The greatest degree of its terms.
Ex. 6z3 + 7z2 – 3z7
The degree of the polynomial is “7”
Which polynomial is represented by?
X2
1
1
X
X
X
1. x2 + x + 1
2. x2 + x + 2
3. x2 + 2x + 2
4. x2 + 3x + 2
5. I’ve got no idea!
To find the degree of a polynomial, find the largest degree of the terms.
8x2  2x + 7
Degrees: 2 1 0
Which is biggest? 2 is the degree!
y7 + 6y4 + 3x4m4
Degrees: 7 4 8
8 is the degree!
Find the degree of x5 – x3y2 + 4
1. 0
2. 2
3. 3
4. 5
5. 10
A polynomial is normally put in ascending or descending order.
What is ascending order?
Going from small to big exponents.
What is descending order?
Going from big to small exponents.
Put in descending order:
1) 8x  3x2 + x4  4
x4  3x2 + 8x  4
2) Put in descending order in terms of x:
12x2y3  6x3y2 + 3y  2x
6x3y2 + 12x2y3  2x + 3y
3) Put in ascending order in terms of y: 12x2y3  6x3y2 + 3y  2x
2x + 3y  6x3y2 + 12x2y3
4) Put in ascending order:5a3  3 + 2a  a2
3 + 2a  a2 + 5a3
Write in ascending order in terms of y:x4 – x3y2 + 4xy – 2x2y3
1. x4 + 4xy – x3y2– 2x2y3
2. – 2x2y3 – x3y2 + 4xy + x4
3. x4 – x3y2– 2x2y3 + 4xy
4. 4xy – 2x2y3 – x3y2 + x4