multiplying and factoring module vii, lesson 2 online algebra vhs@pwcs
TRANSCRIPT
Multiplying and Factoring
Module VII, Lesson 2
Online Algebra
VHS@PWCS
Multiplication Review
1. -2(4x)
2. 3a(5b)
3. 4x(-3x)
4. -4(2x – 3)
1. -8x
2. 15ab
3. -12x2
4. -8x + 12
Try these problems. Before going on with the lesson make sure that you can
get these right.
Multiplying
Problems like -4(2x – 3) use the distributive property to solve.
The distributive property says that-4(2x – 3) = -4(2x) - -4(3)
= -8x + 12
We can use this property to multiply any polynomial by a monomial.5y(8y3 + 7y2 – 3y)
5y(8y3) + 5y(7y2) – 5y(3y)40y4 + 35y3 – 15y2
Try these.
1. 2a(5a3 -7a2 + 2)2a(5a3) – 2a(7a2) + 2a(2)
10a4 – 14a3 + 4a2. -2x(5x + 11)
-2x(5x) + -2x(11)-10x2 – 22x
3. 5m2(m + 7) – 2m(5m2 – 3m + 7)5m2(m) + 5m2(7) + (-2m)(5m2) + (-2m)(-3m) + (-2m)(7)
5m3 + 35m2 +-10m3 + 6m2 + -14m-5m3 + 41m2 – 14m
Now combine all like terms!
Factoring
When two or more numbers are multiplied, each number is a factor of the product.
18(2) = 36
So 18 and 2 are factors of 36
Other factors of 36 are:
1 and 36, 3 and 12, 4 and 9, 6 and 6
Greatest Common Factor
The Greatest Common Factor of two or more numbers is the largest factor that the numbers have in common.
For example:The factors of 54 are:
1, 2, 3, 6, 9, 18, 27, 54The factors of 63 are:
1, 3, 7, 9, 21, 63
The largest factor they have in common is 9, so 9 is the GCF of 54 and 63.
Find the GCF of each pair of numbers.
15 and 50
The factors of 15 are:
1, 3, 5, 15
The factors of 50 are:
1, 2, 5, 10, 25, 50
The largest factor that 15 and 50 have in common is 5, so 5 is their GCF.
88 and 40
The factors of 88 are:
1, 2, 4, 8, 11, 22, 44, 88
The factors of 40 are:
1, 2, 4, 5, 8, 10, 20, 40
The largest factor that 88 and 40 have in common is 8, so 8 is their GCF.
Find the GCF of:12ab and 4a2b2
When variables are involved the GCF will be the GCF of the coefficients and the lowest power of each variable.
The factors of 12 are:1, 2, 3, 4, 6, 12
The factors of 4 are:1, 2, 4
The lowest power of a is 1The lowest power of b is 1Putting all that together the GCF of 12ab and 4a2b2 is
4ab
Find the GCF of the following.
1. 50n4 and 40n3
2. 56x2y and 49xy
3. 12mn, 10mn and 15mn
1. 10n3
2. 7xy
3. mn
Factoring Polynomials
Factoring a polynomial can be done several ways. The first step is always to factor out the
GCF. To do this we must
1. Find the GCF of the terms of the polynomial.
2. Divide each term of the polynomial by the GCF.
3. Write as multiplication.
Factor: 11x + 44x2y
1. Find the GCF of the terms of the polynomial.
The GCF of the terms is 11x
2. Divide each term of the polynomial by the GCF.
3. Write as multiplication.
11x(1 + 4xy)
211 44
11 11
x x y
x x
Try to factor these.
16xy2 – 24y2z + 40y2
1. Find the GCF.
8y2
2. Divide each term by the GCF.
3. Write as multiplication.
8y2(2x – 3z + 5)
28a2 + 21a – 35
1. Find the GCF.
7
2. Divide each term by the GCF.
3. Write as multiplication.
7(4a2 + 3a – 5)
2 2 2
2 2 2
16 24 40
8 8 8
xy y z y
y y y
228 21 35
7 7 7
a a
Wrap-Up
We can use the distributive property to multiply a polynomial by a monomial.
Numbers that are multiplied together are called factors.
Greatest Common Factors are the largest factor that 2 or more numbers have in common.
To factor a polynomial, find the GCF of its terms and divide each term by that GCF. Finally write as multiplication.