5.2 Polynomials Like terms FOIL method.

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Presentation transcript:

5.2 Polynomials Like terms FOIL method

Definition of a Poly Poly- \Pol"y-\ [See Full, a.] A combining form or prefix from Gr. poly`s, many; as, polygon, a figure of many angles; polyatomic, having many atoms; polychord, polyconic. [1913 Webster] Also, polymorphic, polyester, polyamorous.

Definition of a Polynomial A polynomial is an expression made with many constants, variables and exponents, which are combined using addition, subtraction and multiplication, ... but not division.

Degree of a polynomial In a polynomial you find the terms with the highest exponent or addition of exponents; these would be the degree of the polynomial.

Like Terms Terms that are fond of each other Terms with the same variable and exponent. 5x4y3 8x4y3 What can you do with like terms?

Adding Like terms When you add like terms, you add their coefficients. 5x4y3 + 8x4y3 = (5 + 8)x4y3 = 13x4y3 You do not add the exponents. Why?

Adding and Subtracting polynomials Remove the parentheses by distributing the number in front. In this case it is a one. Then add the like terms

What about Subtracting

Multiply Polynomials We use the distributive property to multiply a monomial times binomial, trinomial or any polynomial.

Multiplying a binomial by a binomials Here we double distributive or more often call FOIL

Multiply using FOIL (x – 5)(x + 2) x2 + 2x – 5x – 10 x2 -3x - 10

Multiply using FOIL (x – 5)(x + 2) x2 + 2x – 5x – 10 x2 -3x - 10

Multiply (x + 3)(x2 – 5x + 10)

Multiply (x + 3)(x2 – 5x + 10) x3 – 5x2 + 10x

Multiply (x + 3)(x2 – 5x + 10) x3 – 5x2 + 10x + 3x2 – 15x + 30

Multiply (x + 3)(x2 – 5x + 10) x3 – 5x2 + 10x + 3x2 – 15x + 30

Homework Page 231 – 232 # 17 – 33 odd, # 37 – 45 odd

Homework Page 231 – 232 # 22 – 32 even, # 38 – 50 even