Warm-Up Exercises Warm-up: Homework: Worksheet given in class. #1-20 all.

Warm-Up Exercises Monomial- a number, a variable or the product of a number and one or more variables with whole number exponents. (ex: Degree of a monomial- the sum of the exponents of the variables in the monomials

Warm-Up Exercises Monomial- a number, a variable or the product of a number and one or more variables with whole number exponents. Degree of a monomial- the sum of the exponents of the variables in the monomials

Warm-Up Exercises Binomial- a polynomial with two terms. (the sum of two monomials) Trinomial- a polynomial with three terms. (the sum of three monomials) Polynomial- a monomial or a sum of monomials each called a term. (sum of 4 or more monomials) A polynomial must be written so that the degree of monomials decrease from left to right.

Warm-Up Exercises Rewrite a polynomial I Do Write 15x – x so that the exponents decrease from left to right. Identify the degree and number of terms. What is the leading coefficient of the polynomial? SOLUTION Consider the degree of each of the polynomial’s terms. The polynomial can be written as – x 3 +15x + 3. Degree: 3 Classification: 3 rd degree _ trinomial Number of terms: 3 The leading coefficient is –1. 15x – x 3 + 3

Warm-Up Exercises Rewrite a polynomial EXAMPLE 1 Write 5y – 2y yx 3 so that the exponents decrease from left to right. Identify the degree and number of terms as well as the leading coefficient of the polynomial. 1. You Do for Examples 1,2, and 3 3yx 3 – 2y 2 +5y + 9 Classification: 4 th degree polynomial Degree: 3 Number of terms: 4 Leading Coefficient: 3 ANSWER Tell whether y 3 – 4y is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial. 2. ANSWER polynomial Degree: 3 rd degree binomial

Warm-Up Exercises Tell whether is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial. You Do Identify and classify polynomials 5th degree binomialYes 7bc 3 + 4b 4 c No ; negative exponent n – 2 – 3 No ; variable exponent 6n 4 – 8 n 2nd degree trinomialYes 2x 2 + x – 5 0 degree monomialYes 9 Classify by degree and number of terms Is it a polynomial?Expression a.a. b.b. c.c. d.d. e.e.

Warm-Up Exercises Warm-up- Complete the worksheet from the back of the room Homework: Algebra tiles worksheet.

Warm-Up Exercises Warm-up: Homework: Page 499 #11-35 all. Classify your answers to numbers

Warm-Up Exercises I Do Add polynomials 1. Vertical format: Align like terms in vertical columns. 2x 3 – 5x 2 + x + x 3 + 2x 2 – 1 3x 3 – 3x 2 + x – 1 2. Horizontal format: Group like terms and simplify. (3x 2 + x – 6) + (x 2 + 4x + 10) = = 4x 2 + 5x + 4 (3x 2 + x 2 ) + (x + 4x) + (– )

Warm-Up Exercises EXAMPLE 3 Add polynomials (5x 3 + 2x) + (4x 2 + 3x 3 – 6) Find the sum using the Horizontal and Vertical method. 3. You Do for Example = 8x 3 + 4x 2 + 2x – 6 ANSWER

Warm-Up Exercises I Do Subtract polynomials Find the difference. 4. (4n 2 + 5) – (–2n 2 + 2n – 4) 5.(4x 2 – 3x + 5) – (3x 2 – x – 8)

Warm-Up Exercises Exit Ticket 6. (– 4a 2 + 3a – 1) – (a 2 + 2a – 6) ANSWER –5a 2 + a + 5

Warm-Up Exercises Warm-up: Read and take notes on example 6 and 7 on page 506. Then complete #7 and #8 guided practice. EVERYONE TAKE OUT HOMEWORK TO BE GRADED. Homework: Page 508 #37-42 all and #49-50 all AND page 70 pizzazz. Test Corrections Due Wednesday.

Warm-Up Exercises Warm-up: Algebra Test Prep #7-10 Homework: Page 514 #3-8, 11-18, all.

Warm-Up Exercises Warm-up: Number 11 on packet needs to be completed on a separate sheet of paper. For part b explain in words how you reached your conclusion.

Warm-Up Exercises Warm-up: Fluency Quiz Homework: Page 520 #3, 6, 9, 12, 17, 20, 23, 27, 30, 33, 36, all

Warm-Up Exercises

I Do EXAMPLE 1 Solve (x – 4)(x + 2) = 0. (x – 4)(x + 2) = 0 Write original equation. x – 4 = 0 x = 4 Zero-product property Solve for x. ANSWER The solutions of the equation are 4 and –2. or x + 2 = 0 x = – 2

Warm-Up Exercises Use the zero-product property EXAMPLE 1 CHECK Substitute each solution into the original equation to check. (4  4)(4 + 2) = 0 0  6 = 0 0 = 0 ? ? (  2  4)(  2 + 2) = 0  6  0 = 0 0 = 0 ? ?

Warm-Up Exercises You Do 2. Solve the equation (2x – 6)(x – 1) = 0. ANSWER The solutions of the equation are 3 and 1.

Warm-Up Exercises EXAMPLE 3 I Do The GCF of 4 and 24 is 4. The GCF of x 4 and x 3 is x 3. So, the greatest common monomial factor of the terms is 4x 3. ANSWER 4x x 3 = 4x 3 (x + 6) SOLUTION Factor out the greatest common monomial factor. 4x x 3

Warm-Up Exercises Example 4- You Do Factor out the greatest common monomial factor from 14m + 35n. ANSWER 14m + 35n = 7(2m + 5n)

Warm-Up Exercises EXAMPLE 5 I Do Solve 2x 2 + 8x = 0. 2x 2 + 8x = 0 2x(x + 4) = 0 2x = 0 x = 0 or x + 4 = 0 or x = – 4 ANSWER The solutions of the equation are 0 and – 4. Solve for x. Zero-product property Factor left side. Write original equation.

Warm-Up Exercises EXAMPLE 6 I Do Solve 6n 2 = 15n. 6n 2 – 15n = 0 3n(2n – 5) = 0 3n = 0 n = 0 2n – 5 = 0 n = 5 2 or Solve for n. Zero-product property Factor left side. Subtract 15n from each side. ANSWER The solutions of the equation are 0 and 5 2.

Warm-Up Exercises You Do Solve the equation. ANSWER 0 and – 5 7. a 2 + 5a = s 2 – 9s = 0 ANSWER 0 and x 2 = 2x. ANSWER 0 and

Warm-Up Exercises Factor out the greatest common monomial factor 10) 12a 3 b+15ab 3= 11) 18m 2 n 4 – 12m 2 n 3 +24m 2 n 2= 3ab(4a 2 +5b 2 ) 6m 2 n 2 (3n2-2n+4) 10- I Do, 11- You Do

Warm-Up Exercises Warm-up: On the note card you picked up simplify the expressions. 1.5x + 4(2x + 7) 2.9x – 6(x + 2) + 3 ANSWER 13x + 28 ANSWER 3x – 9