Download 5A Objective: Classify, add, and subtract polynomials Multiply a

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