8.1 Adding and Subtracting Polynomials Objective: SWBAT add and subtract polynomials and classify polynomials by degree and terms.
Mini Quiz 1 1. What is the solution set of the inequality 5 – |x + 4| ≤ -3 a)-2 ≤ x ≤ 6 b) x ≤ -2 or x ≥ 6 c) -12 ≤ x ≤ 4 d) x ≤ -12 or x ≥ 4 The lengths of the sides of a triangle are y, y + 1, and 7 centimeters. If the perimeter is 56 centimeters, what is the value of y? a) 24 b) 25 c) 31 d) 32 What is the solution to the inequality x – 5 > 14? a) x > 9 b) x > 19 c) x < 9 d) x < 19
CAHSEE Review Mean – Average (that’s mean!) Median – Middle Number Mode – Most Often
Overview Classifying Polynomials By Degree Number of Terms Adding Polynomials (combine like terms) Subtracting Polynomials (distribute and combine like terms)
Quick Review x y x2 y3 x2y Sort the following terms: 2x 5y3 -2y 7x 8x2 -3y3 4x2 7x2y -11yx2 -3y -10x2 x y x2 y3 x2y
Monomials…Polynomials Monomial – is a number, a variable, or a product of a number and variable(s) Examples: Polynomial – is a sum of one or more monomials 5; y; 8x2 5 + 7x; y – 4x + 24y2 ; 8y2 – 4xy + x2
Another Standard Form… …the polynomial has the degrees placed in descending order (largest to smallest) 2x3 + 5x2 – 4x + 7 Degree (of polynomial) Leading coefficient Constant term Terms are separated by the +/- signs How many terms does this polynomial have? 4
Name that Degree 2x3 9x + 4x2 – 3 28y + 2y3 + 7y5 – 3x -2xy + 3xy2 – xy3 -3xyz – 4yz3 – x2y2z 3 2 5 4 1 1
Classified by # of terms Name that polynomial! Polynomial Degree Classified by Degree # of terms Classified by # of terms 6 Constant 1 Monomial -2x – 4 1 Linear 2 Binomial -x2 + 3 - x 2 Quadratic 3 Trinomial – 8x2 +4x3 3 Cubic 2 Binomial 3x+2x4 –1+3x2 4 Quartic 4 Polynomial
Adding and Subtracting Polynomials Steps: Distribute (sign changes when it’s minus) Combine Like Terms Simplify: (7x3 – 3x2 + 5) – (2x3 – 5x + 7) 7x3 – 3x2 + 5 5x3 – 2x3 + 5x – 7 - 3x2 + 5x - 2
Adding and Subtracting Polynomials 3x2 + 2x + 1 1. (2x2 + x - 5) + (x + x2 + 6) 2. (3x2 - 5x + 3) - (2x2 - x – 4) 3. (-4x3 + x - 3x2) - (-x2 + 2 – 9x) 4. (5x3 – x + 2x2 + 7) + (3x2 + 7 – 4x) + (4x2 – 8 – x3) 5. (-2x3 - x + 5x2 + 8) - (-2x3 - 4 + 3x) + (7x + 4x2) x2 – 4x + 7 -4x3 – 2x2 + 10x + 2 4x3 + 9x2 – 5x + 6 9x2 + 3x + 12
Wrap Up Classifying Polynomials By Degree Constant (0) Linear (1) Quadratic (2) Cubic (3) Quartic (4) Adding Polynomials (combine like terms) Subtracting Polynomials HW: P. 373 #1-39 odd DLUQ: When you distribute, when does the sign changes? - Number of Terms Monomial (1) Binomial (2) Trinomial (3) Polynomial (4+)