4 ESO Academics - Unit 03 - Exercises 4.3.1 - Polynomials

1. UNIT 03 December
1. Write the degree, the main coefficient and the constant coefficient of the
following polynomials:
a) 𝑷𝑷(𝒙𝒙) = 𝟓𝟓𝒙𝒙𝟐𝟐
+ 𝒙𝒙 − 𝟒𝟒
b) 𝑷𝑷(𝒙𝒙) = 𝒙𝒙𝟐𝟐
+ 𝟑𝟑𝒙𝒙𝟐𝟐
− 𝟒𝟒𝟒𝟒
2. Find 𝑷𝑷( 𝟏𝟏) in 𝑷𝑷(𝒙𝒙) = 𝟑𝟑𝒙𝒙𝟑𝟑
+ 𝟐𝟐𝟐𝟐 − 𝟒𝟒 and 𝑸𝑸(𝒙𝒙) = −𝟐𝟐𝟐𝟐 + 𝟓𝟓.
3. Add, Subtract and multiply the above polynomials
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.1.1

2. UNIT 03 December
4. Extract factors from:
a) 𝟒𝟒𝟒𝟒 + 𝟖𝟖𝟖𝟖
b) 𝟑𝟑𝟑𝟑 + 𝟔𝟔𝟔𝟔 − 𝟗𝟗𝟗𝟗
c) 𝒙𝒙𝟑𝟑
− 𝒙𝒙𝟐𝟐
+ 𝒙𝒙𝟓𝟓
d) 𝒙𝒙𝟓𝟓
− 𝟐𝟐𝒙𝒙𝟒𝟒
+ 𝒙𝒙𝟑𝟑
e) 𝟐𝟐𝒙𝒙𝟐𝟐
− 𝟔𝟔𝟔𝟔 + 𝟒𝟒𝒙𝒙𝟑𝟑
f) 𝟑𝟑𝒙𝒙𝟑𝟑
− 𝟔𝟔𝒙𝒙𝟒𝟒
+ 𝟗𝟗𝒙𝒙𝟐𝟐
g) 𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟔𝟔𝒙𝒙𝟐𝟐
+ 𝟑𝟑
h) 𝟏𝟏𝟏𝟏𝒙𝒙𝟑𝟑
+ 𝟔𝟔𝒙𝒙𝟐𝟐
+ 𝟔𝟔𝟔𝟔
i) 𝒙𝒙𝒙𝒙 − 𝟓𝟓𝟓𝟓𝟓𝟓𝒛𝒛𝟐𝟐
+ 𝟐𝟐𝟐𝟐𝟐𝟐
j) 𝟓𝟓𝒙𝒙𝟐𝟐
− 𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏
5. Write two polynomials of fourth degree from which it can be extracted as
factors:
a) 𝟐𝟐𝟐𝟐𝟐𝟐
b) 𝟑𝟑𝟑𝟑
c) 𝒙𝒙𝟑𝟑
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.1.2

3. UNIT 03 December
d) 𝟐𝟐𝟐𝟐𝒚𝒚𝟐𝟐
6. Which factors can be extracted?
a) (𝒙𝒙 + 𝟏𝟏) ∙ (𝒙𝒙 − 𝟑𝟑) + (𝒙𝒙 − 𝟑𝟑) ∙ (𝒙𝒙 + 𝟐𝟐)
b) (𝒙𝒙 − 𝟐𝟐) ∙ (𝒙𝒙 − 𝟏𝟏) + 𝟑𝟑(𝒙𝒙 − 𝟏𝟏) ∙ (𝒙𝒙 − 𝟐𝟐)
c) 𝟒𝟒(𝒙𝒙 + 𝟒𝟒) ∙ (𝒙𝒙 − 𝟐𝟐) + 𝟔𝟔(𝒙𝒙 − 𝟐𝟐) ∙ (𝒙𝒙 + 𝟐𝟐)
d) (𝒙𝒙 + 𝟐𝟐) ∙ (𝒙𝒙 − 𝟏𝟏) + 𝟑𝟑(𝒙𝒙 − 𝟏𝟏)
e) −𝟐𝟐𝟐𝟐 − 𝟒𝟒 + 𝟐𝟐(𝒙𝒙 + 𝟐𝟐) ∙ (𝒙𝒙 − 𝟑𝟑)
f) 𝟑𝟑(𝒙𝒙 + 𝟏𝟏) + ( 𝟔𝟔 + 𝟔𝟔𝟔𝟔)
g) (𝒙𝒙 + 𝟓𝟓) ∙ (𝒙𝒙 − 𝟐𝟐) + (𝒙𝒙𝟐𝟐
− 𝟒𝟒)
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.1.3

4. UNIT 03 December
http://www.softschools.com/math/algebra/polynomials/classifying_polynomials/
More games on http://www.wartgames.com/themes/math/polynomials.html
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.1.4