Multiplying a binomial by a monomial uses the Distribute property Distribute the 5.
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Transcript of Multiplying a binomial by a monomial uses the Distribute property Distribute the 5.
Lesson 8-2Multiplying and
Factoring Polynomials
Multiplying a binomial by a monomial uses the Distribute property
Multiplying Polynomials
5(𝑥+5)
5(𝑥+5) Distribute the 5
(5 ∙𝑥 )+¿
5 𝑥+25(5 ∙5)
Multiplying Polynomials
−𝑥3 (9 𝑥4−2𝑥3+7 )=¿ ) (7)
What is the simpler form of
A
B
C
D
Solution:
Multiplying two binomial uses the FOIL
Multiplying Polynomials
(3 𝑥−6)(𝑥+5)
¿ (3 𝑥 ∙ 𝑥 )+ (3𝑥 ∙5 )
¿3 𝑥2−6 𝑥+15 𝑥−30
(3 𝑥−6)(𝑥+5)
− (6 ∙𝑥 )−(6 ∙5)
¿3 𝑥2+9 𝑥−30
First Outer Inner Last
Multiplying Polynomials
(𝑥+3)(𝑥+2)
¿ (𝑥 ∙ 𝑥 )+ (𝑥 ∙2 )
¿ 𝑥2+2𝑥+3 𝑥2+6 𝑥
(𝑥+3 𝑥)(𝑥+2)
+(3 𝑥 ∙ 𝑥 )+(3 𝑥 ∙2)
¿ 4 𝑥2+8 𝑥
What is the simpler form of
Multiplying Polynomials
(𝑎+𝑏 )2=(𝑎+𝑏)(𝑎+𝑏)
¿ (𝑎 ∙𝑎)+(𝑎 ∙𝑏)
¿𝑎2+𝑎𝑏+𝑏𝑎+𝑏2
(𝑎+𝑏)(𝑎+𝑏)
+(𝑏 ∙𝑎 )+(𝑏∙𝑏)
¿𝑎2+2𝑎𝑏+𝑏2
What is the simpler form of Special case – Square of a binomial
Factoring Polynomials
Factors: When an integer is written as a product of integers, each of the integers in the product is a factor of the original number.
25 𝑥2=5 ∙5 ∙𝑥 ∙ 𝑥
12=2∙2 ∙3
Factoring PolynomialsGreatest common factor – largest quantity that is a factor of all the integers or polynomials involved.
Find the GCF of each list of numbers.
1) 6, 8 and 46 6 = 2 · 3 8 = 2 · 2 · 246 = 2 · 23 So the GCF is 2
2) 144, 256 and 300144 = 2 · 2 · 2 · 23 · 3256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2300 = 2 · 2 · 3 · 5 · 5 So the GCF is 2 · 2 = 4.
EXAMPLE
Factoring Polynomials
1) x3 and x7
x3 = x · x · xx7 = x · x · x · x · x · x · xSo the GCF is x · x · x = x3
2) 6x5 and 4x3
6x5 = 2 · 3 · x · x · x x · x4x3 = 2 · 2 · x · x · x So the GCF is 2 · x · x · x = 2x3
Find the GCF of each list of terms.
Factoring Polynomials
So the GCF is 5 · x or 5x
What is the GCF terms of
Factoring Polynomials
To factor a polynomial, find the greatest common factor (GCF) of the coefficients and constants and also the GCF of the variables.
Factoring a polynomial reverses the multiplication process. It is writing a polynomial as a product of polynomials.
Then write the polynomial as a product by factoring out the GCF from all the terms.
Factoring PolynomialsWhat is the factored form of
Step 1 – Factor each term
Step 3 - Factoring out of the polynomial
The GCF is Step 2 – Find the GCF
¿𝟒 𝒙 (𝒙𝟒−𝟔 𝒙𝟐+𝟐)
Factoring PolynomialsWhat is the factored form of
Step 1 – Factor each term
Step 3 - Factoring out of the polynomial
The GCF is Step 2 – Find the GCF
¿𝟑 𝒙 (𝟐 𝒙𝟐−𝟑 𝒙+𝟒)
Factoring Polynomials
Remember that factoring out the GCF from the terms of a polynomial should always be the first step in factoring a polynomial.
This will usually be followed by additional steps in the process.