Do Now 3/4/19 Take out your HW from last night. Text p. 410, 2-40 evens, & 41 Copy HW in your planner. Chapter 7 Test Tuesday. Text p. 413, #1-16 all, 19 – textbook only Have you been working on your Review Packet?

Homework Text p. 410, 2-40 evens, & 41

Homework Text p. 410, 2-40 evens, & 41

Learning Goal Learning Target SWBAT simplify, factor, and solve polynomial expressions and equations Learning Target SWBAT review and practice simplifying, factoring, and solving polynomial expressions and equations

Section 7.1 “Add and Subtract Polynomials” Monomial a number, a variable, or the product of a number and one or more variables with whole number exponents -3x Degree = 1 7 Degree = 0 Degree of a Monomial the sum of the exponents of the variables in the monomial Degree = 6 x³yz²

(2x³ – 5x² + x) + (2x² + x³ – 1) Add Polynomials Like Terms terms that have the same variable Add Polynomials (2x³ – 5x² + x) + (2x² + x³ – 1) You can add polynomials using the vertical or horizontal format. Vertical Format Horizontal Format (2x³ + x³) + (2x² – 5x²) + x – 1 2x³ – 5x² + x x³ + 2x² – 1 3x³ – 3x² + x – 1 3x³ – 3x² + x – 1

Subtract Polynomials (4n² + 5) – (-2n² + 2n – 4) Like Terms 4n² + 5 terms that have the same variable (4n² + 5) – (-2n² + 2n – 4) You can subtract polynomials using the vertical or horizontal format. Vertical Format Horizontal Format 4n² + 5 (4n² + 2n²) – 2n + (5 + 4) – (-2n² +2n – 4) +(2n² -2n + 4) 6n² – 2n + 9 6n² – 2n + 9

Section 7.2 “Multiply Polynomials” When multiplying polynomials use the distributive property. Distribute and multiply each term of the polynomials. Then simply. 2x³ (x³ + 3x² - 2x + 5)

“Multiply Using FOIL” (3a + 4) (a – 2) combine like terms

Section 7.4 “Solve Polynomial Equations in Factored Form” Zero-Product Property If ab = 0, then a = 0 or b = 0. The zero-product property is used to solve an equation when one side of the equation is ZERO and the other side is the product of polynomial factors. (x – 4)(x + 2) = 0 The solutions of such an equation are called ROOTS. x + 2 = 0 x – 4 = 0 x = -2 x = 4

Solve Equations By Factoring 2x² + 8x = 0 Factor left side of equation 2x(x + 4) = 0 Zero product property x + 4 = 0 2x = 0 x = -4 x = 0 The solutions of the equation are 0 and -4.

Section 7.5 “Factor x² + bx + c” Factoring x² + bx + c x² + bx + c = (x + p)(x + q) provided p + q = b and pq = c x² + 5x + 6 = (x + 3)(x + 2) Remember FOIL

Factoring polynomials n² – 6n + 8 ‘-’ factors of 8 Sum of factors -8, -1 -8 + (-1)= -9 -2, -4 -2 + (-4) = -6 Find two ‘negative’ factors of 8 whose sum is -6. (n – 2)(n – 4)

Factor by grouping shortcut (1) Split ‘a’ and ‘c’ terms. (2) multiply ‘a’ and ‘c’ together. (3) Then factor the product of ‘a’ and ‘c’ to equal the ‘b’ term. (4) Group terms into binomials. (5) Factor out GCF in both binomials. (6) Factor out common binomial. 1 -120 2 -60 3 -40 4 -30 5 -24 6 -20 8x² – 14x – 15 Add to equal “b” 8x2 – 15 – 20x + 6x Group terms into binomials (8x2 – 20x) + (6x – 15) Factor GCF out each group 4x (2x – 5) + 3 (2x – 5) Factor out the common binomial (2x – 5) (4x + 3)

Section 7.7 “Factor Special Products” You can use the following special products patterns to help you factor certain polynomials. Perfect Square Trinomial Pattern (addition) a² + 2ab + b² (a + b)² (a + b)(a + b) Perfect Square Trinomial Pattern (subtraction) a² – 2ab + b² (a – b)² (a - b)(a - b) Difference of Two Squares Pattern a² – b² (a + b)(a – b)

Section 7.8 “Factor Polynomials Completely” Factor out a common binomial- 2x(x + 4) – 3(x + 4) Factor by grouping- x³ + 3x² + 5x + 15

Factoring Polynomials Completely (1) Factor out greatest common monomial factor. (2) Look for difference of two squares or perfect square trinomial. (3) Factor a trinomial of the form x² + bx + c into binomial factors. (4) Factor a trinomial of the form ax² + bx + c into binomial factors. (5) Factor a polynomial with four terms by grouping. 3x² + 6x = 3x(x + 2) x² + 4x + 4 = (x + 2)(x + 2) 16x² – 49 = (4x + 7)(4x – 7) x² – 7x + 10 = (x – 2)(x – 5) 3x² – 5x – 2 = (3x + 1)(x – 2) -4x² + x + x³ - 4 = (x² + 1)(x – 4)

Problem Solving (16 – w) (w) (w + 4) A box has a volume of 768 cubic inches and all three sides are different lengths. The dimensions of the box are shown. Find the width, length, and height. Volume = length x width x height (16 – w) (w) (w + 4) Substitute the possible solutions to see which dimensions work out. w = 12 w = 8 8 4 8 12 12 16 w = -8 w = 8 w = 12 Volume = 12 x 16 x 4 Can’t have negative width

Clock Partners With your 9:00 partner, complete the Practice Chapter 7 Test #1-27 ODDS, Not #25

Classwork Chapter 7 Practice Test

Classwork Chapter 7 Practice Test

Classwork Chapter 7 Practice Test