Classifying, Adding, Subtracting, Multiplying Polynomials.

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Presentation transcript:

Classifying, Adding, Subtracting, Multiplying Polynomials

Monomials in one variable The product of a constant and a variable raised to a nonnegative integer power. 2x 4 2 is the coefficientdegree is 4 What does it mean to be raised to a nonnegative integer power? The degree of a monomial is found by adding the exponents together!

Monomials: CoefficientDegree 6x 2 Yes 6 3 3x 1/2 Yes 3 1 ½ -√(2) x 3 4x x x 4

Like Terms Two monomials with the same variable raised to the same power. 2x 4 and -5x 4 are like terms Add or subtract like terms using the distributive property. 2x 4 + 5x 4 = (2 + 5)x 4 = 7x 4 2x 4 - 5x 4 = (2 - 5)x 4 = -3x 4

Polynomial: A monomial or the sum of monomials Terms are the monomials that make up the polynomial. 2x 2 yone term monomial 2x 2 y + 5two termsbinomial 5x 2 – 3x + 10 three termstrinomial 2x 5 + 3x 3 -6x + 9four termspolynomial (or more) with 4 terms

Degree of a Polynomial The largest exponent of the polynomial is the degree if the polynomial has only one variable. 5x 2 – 3x + 10degree is 2 The coefficient of the term with the highest exponent is the leading coefficient. 5x 2 – 3x + 10leading coefficient is 5

Name the type of Polynomial. CoefficientsDegree 3x 2 -5Bi 3 2 9y 3 – 2y – 3 Poly /x Z 5 + π (x 2 +1)/(x+5) 5x + √2 3 0

Zero Polynomial and Standard Form Zero Polynomial: If all the coefficients are zero, the polynomial is called the zero polynomial. Standard form: Polynomials are usually written in standard form, beginning with the nonzero term of highest degree and continuing with terms in descending order according to degree. 2x 5 + 4x 4 – 3x 3 – 2x 2 + 6x + 9

Adding Polynomials Find the sum of (8x 3 – 2x 2 + 6x – 2) and (3x 4 – 2x 3 + x 2 + x).

Subtracting Polynomials Find the difference: (3x 4 - 4x 3 + 6x 2 – 1) – (2x 4 - 8x 2 - 6x +5)

Multiplying Polynomials May use the distributive property, FOIL, or Box method… Find the product: a. (x + 3)(x + 1) b. (2x + 1)(3x + 4) Find the product: c. (2x + 5)(x 2 - x + 2) d. (x 2 + 5x – 4)(x 2 – 3x + 2)

Dividing Polynomials Find the quotient: a. 3x 3 – 4x 2 – 7xb. 4x 4 – 8x 3 – 2x x 2x a. Answer: 3x 2 – 4x - 7