lesson 8-2 multiplying and factoring polynomials
DESCRIPTION
Lesson 8-2 Multiplying and Factoring Polynomials. Multiplying Polynomials. Multiplying a binomial by a monomial uses the Distribute property. Distribute the 5. Multiplying Polynomials. What is the simpler form of. A. C. B. D. Solution:. ) (7). Multiplying Polynomials. - PowerPoint PPT PresentationTRANSCRIPT
Lesson 8-2Multiplying and
Factoring Polynomials
Multiplying a binomial by a monomial uses the Distribute property
Multiplying Polynomials
5(π₯+5)
5(π₯+5) Distribute the 5
(5 βπ₯ )+ΒΏ
5 π₯+25(5 β5)
Multiplying Polynomials
βπ₯3 (9 π₯4β2π₯3+7 )=ΒΏ ) (7)
What is the simpler form of
A
B
C
D
Solution:
Multiplying two binomial uses the FOIL
Multiplying Polynomials
(3 π₯β6)(π₯+5)
ΒΏ (3 π₯ β π₯ )+ (3π₯ β5 )
ΒΏ3 π₯2β6 π₯+15 π₯β30
(3 π₯β6)(π₯+5)
β (6 βπ₯ )β(6 β5)
ΒΏ3 π₯2+9 π₯β30
First Outer Inner Last
Multiplying Polynomials
(π₯+3)(π₯+2)
ΒΏ (π₯ β π₯ )+ (π₯ β2 )
ΒΏ π₯2+2π₯+3 π₯2+6 π₯
(π₯+3 π₯)(π₯+2)
+(3 π₯ β π₯ )+(3 π₯ β2)
ΒΏ 4 π₯2+8 π₯
What is the simpler form of
Multiplying Polynomials
(π+π )2=(π+π)(π+π)
ΒΏ (π βπ)+(π βπ)
ΒΏπ2+ππ+ππ+π2
(π+π)(π+π)
+(π βπ )+(πβπ)
ΒΏπ2+2ππ+π2
What is the simpler form of Special case β 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 π₯2=5 β5 βπ₯ β π₯
12=2β2 β3
Factoring PolynomialsGreatest common factor β 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 Β· 3 8 = 2 Β· 2 Β· 246 = 2 Β· 23 So the GCF is 2
2) 144, 256 and 300144 = 2 Β· 2 Β· 2 Β· 23 Β· 3256 = 2 Β· 2 Β· 2 Β· 2 Β· 2 Β· 2 Β· 2 Β· 2300 = 2 Β· 2 Β· 3 Β· 5 Β· 5 So the GCF is 2 Β· 2 = 4.
EXAMPLE
Factoring Polynomials
1) x3 and x7
x3 = x Β· x Β· xx7 = x Β· x Β· x Β· x Β· x Β· x Β· xSo the GCF is x Β· x Β· x = x3
2) 6x5 and 4x3
6x5 = 2 Β· 3 Β· x Β· x Β· x x Β· x4x3 = 2 Β· 2 Β· x Β· x Β· x So the GCF is 2 Β· x Β· x Β· x = 2x3
Find the GCF of each list of terms.
Factoring Polynomials
So the GCF is 5 Β· 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 β Factor each term
Step 3 - Factoring out of the polynomial
The GCF is Step 2 β Find the GCF
ΒΏπ π (ππβπ ππ+π)
Factoring PolynomialsWhat is the factored form of
Step 1 β Factor each term
Step 3 - Factoring out of the polynomial
The GCF is Step 2 β Find the GCF
ΒΏπ π (π ππβπ π+π)
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.