~ Chapter 9 ~ Polynomials and Factoring Algebra I Lesson 9-1 Adding & Subtracting Polynomia ls Lesson 9-2 Mulitplying and Factoring Lesson 9-3 Multiplying Binomials Lesson 9-4 Multiplying Special Cases Lesson 9-5 Factoring Trinomials of the Type x 2 + bx + c Lesson 9-6 Factoring Trinomials of the T ype ax 2 + bx + c Lesson 9-7 Factoring Special Cases Lesson 9-8 Factoring by Grouping Chapter Review Algebra I
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~ Chapter 9 ~ Polynomials and Factoring Algebra I Lesson 9-1 Adding & Subtracting Polynomials Lesson 9-2 Mulitplying and Factoring Lesson 9-3 Multiplying.
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~ Chapter 9 ~Polynomials and Factoring
Algebra I
Lesson 9-1 Adding & Subtracting Polynomials
Lesson 9-2 Mulitplying and Factoring
Lesson 9-3 Multiplying Binomials
Lesson 9-4 Multiplying Special Cases
Lesson 9-5 Factoring Trinomials of the Type x2 + bx + c
Lesson 9-6 Factoring Trinomials of the Type ax2 + bx + c
Lesson 9-7 Factoring Special Cases
Lesson 9-8 Factoring by Grouping
Chapter Review
Algebra I
Adding & Subtracting
Polynomials Cumulative Review Chap 1-8
Lesson 9-1
Adding & Subtracting PolynomialsNotesLesson 9-1
Monomial – an expression that is a number, variable, or a product of a number and one or more variables. (Ex. 8, b, -4mn2, t/3…)
(m/n is not a monomial because there is a variable in the denominator)
Degree of a Monomial
¾ y Degree: 1 ¾ y = ¾ y1… the exponent is 1.
3x4y2 Degree: 6 The exponents are 4 and 2. Their sum is 6.
-8 Degree: 0 The degree of a nonzero constant is 0.
5x0 Degree = ?
Polynomial – a monomial or the sum or difference of two or more monomials.
Standard form of a Polynomial…
Simply means that the degrees of the polynomial terms decrease from left to right.
5x4 + 3x2 – 6x + 3 Degree of each?
The degree of a polynomial is the same as the degree of the monomial with the greatest exponent. What is the degree of the polynomial above?
Adding & Subtracting PolynomialsNotesLesson 9-1
3x2 + 2x + 1 12 9x4 + 11x 5x5
The number of terms in a polynomial can be used to name the polynomial.
Classifying Polynomials
(1)Write the polynomial in standard form.
(2) Name the polynomial based on its degree
(3) Name the polynomial based on the number of terms
6x2 + 7 – 9x4 3y – 4 – y3 8 + 7v – 11v
Adding Polynomials
There are two methods for adding (& subtracting) polynomials…
Method 1 – Add vertically by lining up the like terms and adding the coefficients.
Method 2 – Add horizontally by grouping like terms and then adding the coefficients.
(12m2 + 4) + (8m2 + 5) =
Adding & Subtracting PolynomialsNotesLesson 9-1
(9w3 + 8w2) + (7w3 + 4) =
Subtracting Polynomials
There are two methods for subtracting polynomials…
Method 1 – Subtract vertically by lining up the like terms and adding the opposite of each term in the polynomial being subtracted.
Method 2 – Subtract horizontally by writing the opposite of each term in the polynomial being subtracted and then grouping like terms.
(12m2 + 4) - (8m2 + 5) =
(30d3 – 29d2 – 3d) – (2d3 + d2)
Adding & Subtracting Polynomials
HomeworkLesson 9-1
Homework – Practice 9-1
Multiplying & Factoring Practice 9-1Lesson 9-2
Multiplying & Factoring
Practice 9-1Lesson 9-2
Multiplying & Factoring
Practice 9-1Lesson 9-2
Mulitplying & FactoringNotesLesson 9-2
Distributing a monomial
3x(2x - 3) = 3x(2x) – 3x(3) =
-2s(5s - 8) = -2s(5s) – (-2s) (8) =
Multiplying a Monomial and a Trinomial
4b(5b2 + b + 6) = 4b(5b2) + 4b(b) + 4b(6) =
-7h(3h2 – 8h – 1) =
2x(x2 – 6x + 5) =
Factoring a Monomial from a Polynomial
Find the GCF for 4x3 + 12x2 – 8x
4x3 = 2*2*x*x*x
12x2 = 2*2*3*x*x
8x = 2*2*2*x What do they all have in common? 2*2*x = 4x