The document is a workbook containing various algebraic exercises focusing on polynomials. It includes tasks such as rewriting expressions into polynomials, finding specific values of polynomials, performing polynomial addition and subtraction, and simplification. Additionally, it explores polynomial multiplication and division along with finding their degrees and outputs answers to each activity.

1. 9WORK BOOK

2. POLYNOMIALS

3. Activity 1
Rewrite the following algebraic expressions in to polynomials
𝑎) 28 + 2𝑥
𝑏) 14𝑥 +
C) 35x-24𝑥2
D) 10x-𝑥2

4. Activity 2
Find the values of 𝑝 0 , 𝑝 1 , 𝑝(−1) for the following polynomials
𝑎) 𝑝 𝑥 = 𝑥2
+ 2𝑏) 𝑝 𝑥
= 3𝑥2
− 𝑎𝑥 + 1
𝑐) 𝑝 𝑥 = 4𝑥3
− 24𝑥2
+ 3𝑥
𝑑) 𝑝 𝑥 = 2𝑥2
− 3𝑥 + 1

5. Activity 3
For each pair of polynomials given below find 𝑝 𝑥 + 𝑞(𝑥)
𝑎) 𝑝 𝑥 = 2𝑥2
− 5𝑥 + 1 𝑞 𝑥 = 𝑥2
+ 3𝑥 + 2
𝑏) 𝑝 𝑥 = 𝑥2
+ 𝑥 + 1 𝑞 𝑥 = 𝑥2
+ 𝑥 + 2

6. Activity 4
For each of the following pairs of polynomials find the value of
𝑝 𝑥 − 𝑞(𝑥)
𝑎) 𝑝 𝑥 = 𝑥2
+ 𝑥 𝑞 𝑥 = 𝑥2
− 10𝑥
𝑏) 𝑝 𝑥 = 𝑥2
+ 2𝑥 + 3 𝑞 𝑥 = 2𝑥2
+ 𝑥 + 1

7. Activity 5
Find the value of 𝑝 1 + 𝑞(1) and 𝑝 1 − 𝑞(1) for the following set of polynomials
a) 𝑝 𝑥 = 2𝑥 + 3𝑞 𝑥 = 4𝑥 + 6
b) 𝑝 𝑥 = 2𝑥2 + 5𝑥 + 8 𝑞 𝑥 = 2𝑥2 + 𝑥 + 4

8. Activity6
Find 𝑝 𝑥 𝑞 𝑥 and 𝑝 1 𝑞 1 for the following
a)𝑝 𝑥 = 2𝑥 + 3 𝑞 𝑥 = 3x2
b)𝑝 𝑥 = 𝑥2 + 2𝑥 𝑞 𝑥 = 2𝑥2 + 3𝑥 + 4

9. Activity 7
Simplify the following polynomial as a single polynomial
𝑎) 2𝑥 + 1 3𝑥 + 4 + 2𝑥 − 1 3𝑥 + 4
𝑏) 𝑥 + 1 5𝑥 + 4 + (5𝑥 − 4)(𝑥 + 1)

10. Activity 8
If 𝑝 𝑥 = 𝑥3 − 2𝑥2 + 5𝑥 + 1 and𝑞 𝑥 = 𝑥4-1 then find the
degree of the following.
𝑎) 𝑃(𝑋)𝑏) 𝑞 𝑥
𝑐) 𝑝 𝑥 + 𝑞 𝑥 𝑑) 𝑝 𝑥 − 𝑞 𝑥
𝑒) 𝑝 𝑥 𝑞(𝑥)

11. Activity 9
Find the quotient and remainder on dividing 𝑝 𝑥 by 𝑞 𝑥
𝑎) 𝑝 𝑥 = 6𝑥2 + 7𝑥 + 1 𝑞 𝑥 = 3𝑥 − 1
𝑏) 𝑝 𝑥 = 𝑥2 − 2 𝑞 𝑥 = 2𝑥 − 4

12. ANSWERS
1) a)2𝑥 + 28 𝑏)𝑥2 + 14𝑥 + 40 𝑐)4𝑥3 − 24𝑥2 + 35𝑥 𝑑)𝑥2 + 10𝑥
2) a)𝑃 0 = 1, 𝑃 1 = 0, 𝑃 −1 = 6
b) 𝑝 0 = 1, 𝑝 1 = 3, 𝑝 −1 = 5
c) 𝑝 0 = 0, 𝑝 1 = 17, 𝑝 −1 = −31
d) 𝑝 0 = 2, 𝑝 1 = 3, 𝑝 −1 = 3
3) a) 3𝑥2 − 2𝑥 + 3 𝑏) 2𝑥2 + 2𝑥 + 3
4) a) 11𝑥 𝑏) 𝑥2 − 𝑥 − 2
5) a)𝑝 1 − 𝑞 1 = −5, 𝑝 1 + 𝑞 1 = 15
𝑏)𝑝 1 − 𝑞 1 = 8, 𝑝 1 + 𝑞 1 = 22
6) a) p x q x = 6𝑥2 + 5𝑥 − 6 , 𝑝 1 𝑞 1 = 5
b) 𝑝 𝑥 𝑞 𝑥 = 2𝑥4 + 7𝑥3 + 10𝑥2 + 8𝑥 , 𝑝 1 𝑞 1 = 27
7) a)12𝑥2 + 16𝑥 𝑏)10𝑥2 + 8𝑥
8) a) 3 , b) 4 , c) 4 , d) 4 , e) 7
9) a) 2𝑥 + 3 , 4 𝑏)
1
2
𝑥 + 1 , 2

13. Type equation here.
SUBMITTED BY
RASANATH . V.K
R.NO:29