Section 6.2: Polynomials: Classification, Addition, and Subtraction

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Presentation transcript:

Section 6.2: Polynomials: Classification, Addition, and Subtraction Chapter 6: Polynomials Section 6.2: Polynomials: Classification, Addition, and Subtraction

Section 6.2: Polynomials: Classification, Addition, and Subtraction Goal: To classify, add, and subtract polynomials

Section 6.2: Polynomials: Classification, Addition, and Subtraction Monomial – polynomial with one term Ex: 2x -5 3xyz ½ a Binomial – polynomial with 2 terms 2x + 3 -5x – 12 x2 + 4 Trinomial - polynomial with 3 terms 7x2 + 8x – 1 ½ x + 3y – 2z

Section 6.2: Polynomials: Classification, Addition, and Subtraction Degree – To determine the degree of a monomial, add the exponents for each variable Degree of a polynomial – the degree of the monomial with the greatest degree. 3430r2 +6860r +3430 has a degree of 2 Leading coefficient - coefficient of the first term Standard form

Section 6.2: Polynomials: Classification, Addition, and Subtraction Example 1 Determine whether each expression is a polynomial. If it is a polynomial, state the degree of a the polynomial. c4 – 4√c + 18 -16p5 + ¾ p2q7

Section 6.2: Polynomials: Classification, Addition, and Subtraction Example 2 Polynomial Degree Classified by degree Classified by number of terms -5 ¼ x -9x + 2 x2 – 6 -x3 + 2x + 1 3x4 + 2x3 – x2 + 5x – 8

Section 6.2: Polynomials: Classification, Addition, and Subtraction To add or subtract polynomials, add and subtract the like terms Same variable, same exponent

Section 6.2: Polynomials: Classification, Addition, and Subtraction Example 3 Find the sum. Write the answer in standard form. (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3) (6x2 – x + 3) + (-2x + x2 – 7)

Section 6.2: Polynomials: Classification, Addition, and Subtraction Example 4 Find the difference. Write the answer in standard form. (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1) (4x2 – 1) – (3x – 2x2) (12x – 8x2 + 6) – (-8x2 – 3x + 4)

Section 6.2: Polynomials: Classification, Addition, and Subtraction Example 2 Simplify each expression (2a3 + 5a – 7) – (a3 – 3a + 2) (4x2 – 9x + 3) + (-2x2 – 5x – 6)

Section 6.2: Polynomials: Classification, Addition, and Subtraction Example 5 The first floor of a home has the floor plan shown below. Find an expression in standard form for the area of the first floor.

Section 6.2: Polynomials: Classification, Addition, and Subtraction Homework: Practice Exercises Pg. 262 #2-30 (even), 39, 40