Polynomial Functions Addition, Subtraction, and Multiplication.

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Presentation transcript:

Polynomial Functions Addition, Subtraction, and Multiplication

Definitions Monomial – real number, variable, or a product of the two  Degree – exponent of the variable Polynomial – a monomial or the sum of monomials.  Degree of a polynomial – largest degree of any term of the polynomial

Notation Example: P(x) = 2x 3 +3x 2 -x+1 Standard Form of a Polynomial:  Polynomial function written in descending order by degree Polynomial function:

5x 2 Find Common Terms: Adding Polynomials Add coefficients of like terms: Example: Polynomial 4x 2 +2x 3 +13x + x 2 +8x 3 +9 Add: 5x 2 +10x 3 +13x+9 Standard Form: 10x 3 +5x 2 +13x+9 ( ) ( ) 4x 2 +x 2 +2x 3 +8x 3 +13x +9+10x 3

Subtracting Polynomials Distribute negative sign, find common terms and add/subtract:  Example Polynomial (6x 4 -2x 3 -4x 4 )-(x 2 +7x 3 +1) Distribute 6x 4 -2x 3 -4x 4 -x 2 -7x 3 -1 Find Common Terms: Add/Subtract: 2x 4 -9x 3 -x 2 -1 Standard Form: 2x 4 -9x 3 -x x 4 -4x 4 -2x 3 -7x 3 -x 2 -12x 4 -9x 3

+1 ( )(x 2 +5x+6)+1 Multiply: x 3 +5x 2 +6x+x 2 +5x+6 Multiplying Polynomials Generally distribute and simplify by addition or subtraction Example: Standard Form: x 3 +6x 2 +11x+6 x(x 2 +5x+6) xPolynomial: Distribute: Add Common Terms:x x 2 +x 2 +6x +5x+6x 2 +11x

SPECIAL PATTERNS SUM & DIFFERENCE

BINOMIAL SQUARED