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Polynomials
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Unit 2: Algebra Investigation
MM1A2c: Add, subtract, multiply, and divide polynomials. Essential Question: How do you add and subtract polynomials?
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What does each prefix mean?
mono one bi two tri three
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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.
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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)
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State whether each expression is a polynomial. If it is, identify it.
1) 7y - 3x + 4 trinomial 2) 10x3yz2 monomial 3) not a polynomial
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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”
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Find the degree of each monomial.
1) 5x2 2 4a4b3c 8 -3
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Degree of a Polynomial The greatest degree of its terms.
Ex. 6z3 + 7z2 – 3z7 The degree of the polynomial is “7”
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Which polynomial is represented by?
X 1 X 1 X2 X x2 + x + 1 x2 + x + 2 x2 + 2x + 2 x2 + 3x + 2 I’ve got no idea!
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Which is biggest? 2 is the degree!
To find the degree of a polynomial, find the largest degree of the terms. 8x2 - 2x + 7 Degrees: Which is biggest? 2 is the degree! y7 + 6y4 + 3x4m4 Degrees: 8 is the degree!
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Find the degree of x5 – x3y2 + 4
2 3 5 10
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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.
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Put in descending order:
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
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3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x
-2x + 3y - 6x3y2 + 12x2y3 Put in ascending order: 5a a - a2 -3 + 2a - a2 + 5a3
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Write in ascending order in terms of y: x4 – x3y2 + 4xy – 2x2y3
– 2x2y3 – x3y2 + 4xy + x4 x4 – x3y2– 2x2y3 + 4xy 4xy – 2x2y3 – x3y2 + x4
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