Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
5A Objective: Resources: Classify, add, and subtract polynomials Multiply a monomial by a polynomial Prentice Hall Algebra 1, 2011: 8.1 & 8.2 p474-485 WORKSHEET NOTES: Monomials & Like Terms A.APR.1 MP1, MP3, MP6 CC Standards: Math Practices: Vocab/Concepts: monomial – p474 a real number, a variable, or a product of a real number and one or more variables with whole number {0, 1, 2, 3, … } exponents; think… single term polynomial polynomial – p475 the sum or difference of one or more monomials o 1 non-like term monomial o 2 non-like terms binomial o 3 non-like terms trinomial NOTE: a quotient with a variable in the denominator is not a polynomial degree of a monomial (term) – p475 the sum of the exponents of the variable of a monomial NOTE: 0 has no degree degree of a polynomial – p475 the highest degree of any term of the polynomial o degree 0 (non-zero) constant (c = c0) o degree 1 linear o degree 2 quadratic o degree 3 cubic o degree 4 quartic o degree 5 quintic standard form of a polynomial in one variable: an xn + an-1 xn-1 + an-2 xn-2 + … a2 x2 + a1 x + a0 (an, an-1, an-2, …, a2, a1, a0 are coefficients) use distributive property to multiply a monomial by a polynomial Practice: [5A1] 8.1 p477 (9-51 odd); [5A2] 8.2 p483 (9-13 odd, 29-33 odd) 5B Objective: Multiply two binomials or a binomial by a trinomial Find the square of a binomial and to find the product of a sum and difference Prentice Hall Algebra 1, 2011: 8.3 & 8.4 p486-497 A.APR.1 MP1, MP2, MP3, MP7, MP8 Resources: CC Standards: Math Practices: Practice: FOIL Method (first, outer, inner, last) (a + b) (c + d) = ac + ad + bc + bd Another method for multiplying polynomials together is using a vertical approach – see p 489 Practice: [5B1] 8.3 p489 (11-17 odd, 23-27 odd, 31-41 odd, 42, 47); [5B2] 8.4 p495 (9, 13, 17, 21, 25-31 odd, 37, 41, 45, 47) 5C Objective: Factor a monomial from a polynomial Factor trinomials of the form x2 + bx + c Resources: Prentice Hall Algebra 1, 2011: 8.2 p480-484; 8.5 p500-505 WORKSHEETS: Factor Polynomials Starter 1 & 2, Factor Polynomials A & B CC Standards: A.APR.1, A.SSE.1a, Math Practices: MP1, MP2, MP3, MP7 Vocab/Formulas/Concepts: Basic Steps to Factoring o ALWAYS pull out the greatest common factor o For quadratics: Find a, b, and c of the remaining quadratic standard form ax2 + bx + c Need two numbers whose product = ac & sum = b Use the two numbers to break up the middle term Use grouping method with first two terms and last two terms Practice: [5C1] Day A: 8.2 p483 (15-27 odd, 37, 39) [5C2] Day A: WORKSHEET Factor Polynomials A [5C3] Day B: WORKSHEET Factor Polynomials B 5D Objective: Resources: Factor perfect-square trinomials and the differences of two squares Prentice Hall Algebra 1, 2011: 8.7 p511-516 WORKSHEETS: Factor Special Cases & Polynomials Deluxe CC Standards: A.SSE.1, A.SSE.1a, A.SSE.1b, A.SSE.2 Math Practices: MP1, MP2, MP3 Vocab/Formulas/Concepts: Special Quadratic Cases o perfect square trinomial: p511 x2 + 2xy + y2 = (x + y)2 x2 – 2xy + y2 = (x – y) 2 the two numbers (from the sum and product of the coefficients) will be the same value o difference of two squares: p513 x2 – y2 = (x + y)(x – y) the two numbers (from the sum & product of the coefficients) will be opposite values Practice: [5D1] DAY B: WORKSHEET Factor Special Cases [5D2] DAY C: WORKSHEETS Factoring Polynomials Deluxe 1 [5D3] DAY C: WORKSHEETS Factoring Polynomials Deluxe 2; [5D4] DAY D: 8.7 p515 (25, 29, 33, 37, 59) Alternate Practice: 8.7 p514 (9-39 1st column, 42, 47, 49, higher degree 55-58) [UNIT REVIEW – Part 1] Free Response Review: 1-55 Multiple-Choice Review: 1-20 5E Objective: Factor higher-degree polynomials by grouping Resources: Prentice Hall Algebra 1, 2011: 8.8 p517-521 CC Standards: A.SSE.1, A.SSE.1a, A.SSE.1b, A.SSE.2 Math Practices: MP1, MP2, MP3, MP7 Vocab/Formulas/Concepts: Grouping is similar to prior method as before… think of the terms already pre-broken up A factor you found may need to be factored. Is the factor a difference of two squares perhaps? Practice: [5E1] DAY D: 8.8 p519 (9-25 1st column, 28-30, 31, 33, 35, 41, 43, challenge 37) 5F Objective Long divide a polynomial Resources: Prentice Hall Algebra 1, 2011: 11.3 p666-671 CC Standards: APR.D.6 Math Practices: MP1, MP2, MP3, MP7 Vocab/Formulas/Concepts: Dividing a polynomial by a polynomial (see example below) 1. Arrange terms of dividend and divisor in general form. If term is missing from, add the terms with a coefficient of 0 2. Divide first term of dividend by first term of divisor. This is first term of quotient. 3. Multiply first term of quotient by whole divisor and place product under the dividend 4. Subtract this product from the dividend. (It easier to instead rewrite as an addition problem after changing the signs of the product.) 5. Bring down the next term. o Repeat steps 2 thru 5 as necessary until degree of remainder is less than degree of divisor Practice: [5F1] WS - Long Division of Polynomials EXAMPLE: Use polynomial long division to divide 2x2 + 6x 7 by x + 1 Step 1 To find the first term of the quotient, divide the highest-degree term of 2x2 + 6x + 7 by the highest-degree term of the divisor, x + 1. Circle these terms before dividing. Step 2 Multiply x + 1 by the new term, 2x, in the quotient. 2x(x + 1) = 2x2 + 2x. Align like terms. Step 3 Subtract to get 4x. Bring down the next term, 7. Step 4 Divide the highest-degree term of 4x + 7 by the highest-degree term of x + 1. Circle these terms before dividing. Step 5 Repeat Steps 2 and 3. The remainder is 3 because its degree is less than the degree of x + 1. 5G Objective Synthetically divide a polynomial by the binomial (x – a) Resources: Prentice Hall Algebra 2, 2011: 5.4 CC Standards: APR.B.2, APR.D.6 Math Practices: MP1, MP2, MP3, MP7 Vocab/Formulas/Concepts: Synthetic division Used to divide a polynomial P(x) by binomial (x – a) see example below Remainder Theorem The value of P(a) is equivalent to the remainder when polynomial P(x) is divided by x – a. Practice: [5G1] WS - Synthetic Division of Polynomials EXAMPLE: Use synthetic division to divide x3 + 13x2 + 46x + 48 by x + 3. Step 1 Set up your polynomial division. (x3 + 13x2 + 46x + 48) (x + 3) Step 2 Reverse the sign of the constant, 3, in the divisor. Write the coefficients of the dividend: 1 13 46 48. Step 3 Bring the first coefficient, 1, down to the bottom line. Step 4 Multiply the coefficient, 1, by the divisor, –3. Put this product, 3, underneath the second coefficient 13, and add those two numbers: 13 + (3) = 10. Step 5 Continue multiplying and adding through the last coefficient. The final sum is the remainder. If dividing by polynomial (mx – a), then divide all terms of the polynomial and the divisor by m. Use a/m in the box. [UNIT REVIEW – Part 2] Free Response Review: 56-75 Multiple-Choice Review: 21-25 (revisit 11-20) on Moodle: WS Extra Factoring Problems