By: William & Loc
 Multiply a polynomial by a monomial.
 Factor a monomial out of a polynomial.
 Finding Greatest Common Factors.
A(b + c) = ab + ac
-4y²(5y - 3y)
Use the Distributive Property
-20y³ + 12y³
Add coefficients and exponents with the
+
same base- Example: -4y²(5y³)= 20y² ³
Solve
1) 3m(m + 6)
2) 5b²(b + 4)
1) 3m² + 18m
2) 5b³ + 20b²
 1) 4b(5b² + b + 6)
 2) -7h(3h² - 8h – 1)
1)20b³ + 4b² + 24b
2)-21h³ + 56h²+ 7h
 GCF stands for 3 words:
◦ Greatest,
◦ Common and,
◦ Factor.

Factors are the numbers you multiply together to get another number:
 2x3=6
 2 = factor
 3 = factor
◦ Sometimes we want to find ALL the factors of a number:
The factors of 12 are 1, 2, 3, 4, 6 and 12 ...
... because 2 × 6 = 12, or 4 × 3 = 12, or 1 × 12 = 12.

Let say you have worked out the factors of two or more numbers:

Example:
_The factors of 12 are 1, 2, 3, 4, 6 and 12
_The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
Then the common factors are those that are found in both lists (1,2,3 and 6).
 What
are the common factors of 15, 30 and 105?

The factors of 15 are 1, 3, 5, and 15

The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.
=> The common factors are 1, 3, 5 and 15. <=
 It is simply the largest of the common factors.
 The GFC is the largest of the common factors of
2 or more numbers

Find the GCF of 36 and 54:
◦ The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
◦ The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

The common factors of 36 and 54 are: 1, 2, 3, 6, 9, 18.
=> GCF of 36 and 54 is 18.

One of the most useful thing is when we want to simplify a fraction:
◦ Example: How can we simplify 12/30?
◦ Common Factors of 12 and 30 were 1, 2, 3 and 6,
◦ The Greatest Common Factor is 6.
◦ The largest number we can divide both 12 and 30 evenly by is 6:
12/30 = 2/5 (12 : 6 and 30 : 6)
Two
numbers
6 & 18
All factors
6: 1,2,3,4,6
18: 1,2,3,6,9,18
Common
factors
GCF
Simplify
fraction
1, 2, 3, 6
6
6/18 = 1/3
 Find the GCF of the terms of 4x³ +
12x² - 8x
 List the prime factors of each term. Identify the
factors common to all terms:
◦ 4x³ = 2 . 2 . x . x . x
◦ 12x² = 2 . 2 . 3 . x . x
◦ 8x = 2 . 2 . 2 . x
=> The GCF is 2 . 2 . x or 4x <=
Two
numbers
24 & 108
All factors
2 × 2 × 2 × 3 = 24, and
2 × 2 × 3 × 3 × 3 = 108
GCF
Simplify
fraction
2 × 2 × 3 = 12
6/18 = 1/3
Now let’s factor a monomial from a polynomial
 Factor 3x³ - 12x²
 First, find the GCF
3x³ = 3 · x · x · x
12x² = 2 · 2 · 3 · x · x Here, the GCF is 3x
Lastly, factor out the monomial
 => 3x(x²) + 3x(-4x) <= Factor 3x from each term
 =>3x(x² - 4x) <= Final answer

 Use the GCF to factor the polynomials
below.
 8x² - 12x
 5d³ + 10d
1) 4x(2x – 3)
2) 5d(d² + 2)
 Tutorial:
 You guys are to be divided into 4 teams.
 A set of questions will appear on the board.
 The team to answer all the questions on the
board first will win points according to the
slide.(Try to fit all answers on your board, and in
the order)
 The team to score the most points at the end of
the game wins! (You guys keep score)
 On the Board
On your team’s board
 1) problem
1) answer
 2) problem
2) answer
 3) problem
3) answer
1) (x + 8)2x
2) (3y + 5)6y
3) 9m(m + 6)
4) Find the GCF of the terms of 15w + 21w
1) 9m(2m + m + 4)
2) Find the GCF of the terms of: 5t² - 10
3) Factor out: 6x5 + 31x8
4) Factor out: y3 + 6y
1) -5x(8x² – 7 + 3x³)
2) 2n(4n + 5n + 8)
3) -10k(9k – 3k² - 6)
4) Factor out: 5p4 – 5p
 1) Factor out: 8x2 + 2x – 18
 2) 12c(-5c² + 3c – 4)
 3) 3k(-7k - 2k + 5k³)
 Factor out #’s 1-3
 1) 7x2 + 21x + 56
 2) 19y7 + 5y7
 3) 6x5 + 31x8
 4) (4a² – 7a – 8)2a
2 + 2= ?
Thanks for
listening!