1. Naming Polynomials Add and Subtract Polynomials Multiply Polynomials
U2 – Polynomials
Naming Polynomials
Add and Subtract Polynomials
Multiply Polynomials

2. Definitions Exponents Power Simplify Terms Monomials Polynomials
Exponents: the power attached to the base
Power: the number that is the exponent written in the form xª
Simplify: rewrite expression without parenthesis or negative exponents
Terms: Each number or variable/number or variable in an expression
Monomials: some algebraic expressions with exponents.
Polynomials: Monomial or group of monomials.

3. More Definitions Like Terms Constant Degree Coefficient Binomial
Trinomial
Like Terms: two monomials that are the same or differ only by their coefficient.
Constant: monomials that contain no variable
Degree: sum of exponents on variables of one monomial
Coefficient: Number in front of the variables
Binomial: expression with 2 unlike terms
Trinomial: expression with 3 unlike terms

4. a. 2 𝒑 𝟒 + 5 𝒑 𝟑 EXAMPLE 1 Identify polynomial functions
Name each polynomial by degree (highest exponent), the number of terms (and expression that can be written as a sum, the parts added together) leading coefficient (number in front of the variable with highest degree)
a. 2 𝒑 𝟒 + 5 𝒑 𝟑
SOLUTION
a. The degree is 4, number of terms is 2, leading coefficient 2

5. a. 10a EXAMPLE 1 Identify polynomial functions
Name each polynomial by degree, the number of terms, and leading coefficient.
a. 10a
SOLUTION
a. The degree is 1, the number of terms is 1, and the leading coefficient is 10.

6. a. - 5 𝒏 𝟑 +10n - 2 EXAMPLE 1 Identify polynomial functions
Name each polynomial by degree, the number of terms, leading coefficient
a 𝒏 𝟑 +10n - 2
SOLUTION
a. The degree is 5, the number of terms is 3, and the leading coefficient is 3.

7. a. 3 EXAMPLE 1 Identify polynomial functions
Name each polynomial by degree, the number of terms, and leading coeffcient.
a. 3
SOLUTION
a. The degree is :None and the number of terms is 1, leading coefficient none.

8. 1. f (x) = 13 – 2x GUIDED PRACTICE for Examples 1 and 2
State the polynomials degree, terms, and leading coefficient.
f (x) = 13 – 2x
SOLUTION
It is a polynomial function.
Standard form: – 2x + 13
Degree: 1
Leading coefficient of – 2.
Number of terms : 2
f (x) = – 2x + 13

9. 2. p (x) = 9x4 – 5x 2 + 4 GUIDED PRACTICE for Examples 1 and 2
It is a polynomial function.
Standard form: p (x) = 9x4 – 5x 2 + 4
Degree: 4
Leading coefficient of 9.
Number of terms : 4
SOLUTION

10. 3. h (x) = 6x2 + π – 3x GUIDED PRACTICE for Examples 1 and 2 SOLUTION
The function is a polynomial function that is already written in standard form will be 6x2– 3x + π .
It has degree 2 and a leading coefficient of 6.
It is a polynomial function.
Standard form: 6 𝑥 2 – 3x + π
Degree: 2
Terms: 3
Leading coefficient of 6

11. x3 + 6x2 + 11 in a vertical format.
EXAMPLE 1
Add polynomials vertically and horizontally
Add 2x3 – 5x2 + 3x – 9 and
x3 + 6x in a vertical format.
SOLUTION
a x3 – 5x2 + 3x – 9
+ x3 + 6x
3x3 + x2 + 3x + 2

12. b. Add 3y3 – 2y2 – 7y and – 4y2 + 2y – 5 in a horizontal format.
EXAMPLE 1
Add polynomials vertically and horizontally
b. Add 3y3 – 2y2 – 7y and – 4y2 + 2y – 5 in a horizontal format.
(3y3 – 2y2 – 7y) + (– 4y2 + 2y – 5)
= 3y3 – 2y2 – 4y2 – 7y + 2y – 5
= 3y3 – 6y2 – 5y – 5

13. EXAMPLE 2
Subtract polynomials vertically and horizontally
a. Subtract 3x3 + 2x2 – x + 7 from 8x3 – x2 – 5x + 1 in a vertical format.
8x3 – x2 – 5x + 1
– (3x3 + 2x2 – x + 7)
8x3 – x2 – 5x + 1
+ – 3x3 – 2x2 + x – 7
5x3 – 3x2 – 4x – 6
SOLUTION
a. Align like terms, then add the opposite of the
subtracted polynomial.

14. 4z2 + 9z – 12 in a horizontal format.
EXAMPLE 2
Subtract polynomials vertically and horizontally
Subtract 5z2 – z + 3 from
4z2 + 9z – 12 in a horizontal format.
(4z2 + 9z – 12) – (5z2 – z + 3) = 4z2 + 9z – 12 – 5z2 + z – 3
= 4z2 – 5z2 + 9z + z – 12 – 3
= – z2 + 10z – 15
Write the opposite of the subtracted polynomial,
then add like terms.

15. 1. (t2 – 6t + 2) + (5t2 – t – 8) GUIDED PRACTICE for Examples 1 and 2
Find the sum or difference.
1. (t2 – 6t + 2) + (5t2 – t – 8)
t2 – 6t + 2
+ 5t2 – t – 8
SOLUTION
6t2 – 7t – 6

16. 2. (8d – 3 + 9d3) – (d3 – 13d2 – 4) GUIDED PRACTICE
for Examples 1 and 2
2. (8d – 3 + 9d3) – (d3 – 13d2 – 4)
= (8d – 3 + 9d3) – (d3 – 13d2 – 4)
= (8d – 3 + 9d3) – d3 + 13d2 + 4)
SOLUTION
= 9d3 –3 d3 + 13d2 + 8d – 3 + 4
= 8d3 + 13d2 + 8d + 1

17. ( 3 𝑋 2 - 5 ) + ( 7 𝑋 2 - 3 ) ( 5 𝐶 2 + 7c + 3 ) + ( 𝑐 2 + 6c + 4 )
TRY THE FOLLOWING PROBLEMS
( 3 𝑋 ) + ( 7 𝑋 )
( 5 𝐶 c + 3 ) + ( 𝑐 c + 4 )
( − 𝑥 𝑥 𝑥 x + 2) +
( 𝑥 3 + 𝑥 𝑥 )

18. ANSWERS TO ADDITION PROBLEMS
( 3 𝑋 ) + ( 7 𝑋 ) = 10 𝑋
( 5 𝐶 c + 3 ) + ( 𝑐 c + 4 ) = 6 𝑥 c + 7
( − 𝑥 𝑥 𝑥 x + 2) + ( 𝑥 3 + 𝑥 𝑥 )
= 11 𝑥 5 −𝑥 −𝑥 x + 6

19. ( 4 𝑋 2 - 9 ) - ( 2 𝑋 2 - 3 ) ( 4 𝐶 2 + 2c + 6 ) - ( 𝑐 2 + 8c + 4 )
TRY THE FOLLOWING PROBLEMS
( 4 𝑋 ) - ( 2 𝑋 )
( 4 𝐶 c + 6 ) - ( 𝑐 c + 4 )
( − 2𝑥 𝑥 𝑥 x + 9 ) -
( - 𝑥 3 + 𝑥 𝑥 )

20. ANSWERS TO THE SUBTRACT PROBLEMS
( 4 𝑋 ) - ( 2 𝑋 ) = 2𝑥
( 4 𝐶 c + 6 ) - ( 𝑐 c + 4 ) = 3 𝑐 2 +6𝑐+2
( − 2𝑥 𝑥 𝑥 x + 9 ) - ( - 𝑥 3 + 𝑥 𝑥 )
= −2𝑥 5 −2𝑥 4 −8𝑥 3 -3x + 4

21. Multiply Polynomials 3(2) 2.3(2x) 3.3x(2x) 4.3x(2x+1)