Mathematics 8

1. Polynomial
Dissection
CHAPTER 1

2. Factoring
Polynomials with a
Common Factor

3. What is a Factor?
A factor is one of two or
more numbers that
divides a given number
without a remainder.

4. Example:
What are the factors of 10?
1, 2, 5, 10
What are the factors of 20?
1, 2, 4, 5, 10, 20

5. What is a GCF?
A GCF (Greatest
Common Factor) is the
greatest factor that is
common to two or

6. 1. What is the
GCF of 10 and
15?
10 = 1, 2, 5, 10
15= 1, 3, 5, 15
2. What is the
GCF of 18 and
30?
18= 1, 2, 3, 6, 9, 18
30= 1, 2, 3, 5, 6, 10,
15, 30
Example:

7. 3. What is the GCF of
𝟏𝟒𝒃 𝟐
, 𝟐𝟖𝒃 and 𝟑𝟓𝒃 𝟑
?
𝟏𝟒𝒃 𝟐
= 𝟐 ∙ 𝟕 ∙ 𝒃 ∙ 𝒃
𝟐𝟖𝒃 = 𝟐 ∙ 𝟐 ∙ 𝟕 ∙ 𝒃
𝟑𝟓𝒃 𝟑
= 𝟓 ∙ 𝟕 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃
𝑮𝑪𝑭 = 𝟕𝒃
Example:

8. A Polynomial is an expression
consisting of variables and
coefficients, that involves only the
operations of addition, subtraction,
multiplication, and non-negative
integer exponentiation of variables.
What is Polynomial?

9. 1. 𝟖𝒙 + 𝟐𝟖
Example:
2. 𝟏𝟏𝒙 𝟐
𝒚 𝟑
+ 𝟐𝟐𝒙 𝟑
𝒚 𝟐
− 𝟒𝟒𝒙 𝟒
𝒚 𝟒
3. 𝟐𝟔𝒄 𝟐
+ 𝟑𝟗𝒄
4. 𝟏𝟔𝒕 𝒔 + 𝒗 + 𝟒𝟎 𝒔 + 𝒗

10. 1. 𝑴𝒐𝒏𝒐𝒎𝒊𝒂𝒍
Types of Polynomials
2. 𝑩𝒊𝒏𝒐𝒎𝒊𝒂𝒍
3. 𝑻𝒓𝒊𝒏𝒐𝒎𝒊𝒂𝒍
4. 𝑴𝒖𝒍𝒕𝒊𝒏𝒐𝒎𝒊𝒂𝒍

11. How to factor polynomials with
a common factor?
Factoring is the reverse of
multiplication.The Distributive Property is used to
factor out the GCF of the terms in a
polynomial and to write the
polynomial in factored form.

12. The Distributive Property states
that
𝑎𝑏 + 𝑎𝑐 = 𝑎 𝑏 + 𝑐
Example:
8𝑥 + 28
4 ∙ 2𝑥 + 4 ∙ 7
𝟒 𝟐𝒙 + 𝟕
Find the GCF of 8 and 28.
The GCF of 8 and 28 is 4.


13. STEPS IN FACTORING
POLYNOMIALS1. Find the GCF of the numerical
coefficients.
2. Check the variable which appears in all
the terms. If a variable appears in all
the terms, choose the lowest degree
for each variable.
3. Divide each term by the GCF.
4. Write the factored form.

14. Factor 𝟏𝟏𝒙 𝟐
𝒚 𝟑
+ 𝟐𝟐𝒙 𝟑
𝒚 𝟐
−
𝟒𝟒𝒙 𝟒
𝒚 𝟒
𝟏𝟏𝒙 𝟐 𝒚 𝟑 = 𝟏𝟏 ∙ 𝒙 ∙ 𝒙 ∙ 𝒚 ∙ 𝒚 ∙ 𝒚
+𝟐𝟐𝒙 𝟑 𝒚 𝟐 = 𝟏𝟏 ∙ 𝟐 ∙ 𝒙 ∙ 𝒙 ∙ 𝒙 ∙ 𝒚 ∙ 𝒚
−𝟒𝟒𝒙 𝟒 𝒚 𝟒 = 𝟏𝟏 ∙ 𝟒 ∙ 𝒙 ∙ 𝒙 ∙ 𝒙 ∙ 𝒙 ∙ 𝒚 ∙ 𝒚 ∙ 𝒚 ∙ 𝒚
Example 1:
= 𝟏𝟏𝒙 𝟐 𝒚 𝟐 𝒚 + 𝟐𝒙 −𝟒𝒙 𝟐
𝒚 𝟐

15. Factor 𝟐𝟔𝒄 𝟐
+ 𝟑𝟗𝒄
𝟐𝟔𝒄 𝟐
= 𝟐. 𝟏𝟑. 𝒄. 𝒄
+ 𝟑𝟗𝒄 = 𝟑. 𝟏𝟑. 𝒄
= 𝟏𝟑𝒄 𝟐𝒄 + 𝟑
Example 2:

16. Factor 𝟏𝟔𝒕 𝒔 + 𝒗 + 𝟒𝟎 𝒔 + 𝒗
𝟏𝟔𝒕 𝒔 + 𝒗 = 𝟐𝒕 ∙ 𝟖 ∙ 𝒔 + 𝒗
+𝟒𝟎 𝒔 + 𝒗 = 𝟓 ∙ 𝟖 ∙ 𝒔 + 𝒗
= 𝟖 𝒔 + 𝒗 + 𝟐𝒕 + 𝟓
Example 3: