1. Sec Math II
1.3

2. Polynomials

3. Nomial: A name or term
Monomials: x 3 7x Binomials: x +2 2x – 3 7 𝑥 Trinomial: 3 𝑥 2 + 5x – 2 −5 𝑥 2 +4𝑥 +6

4. Polynomials POLY nomials
Many terms each with the same variable raised to an integer power. 3 𝑥 2 + 5x 𝑥 𝑥 𝑥 2 + 2x + 9

5. Which look better to you ?
𝟑 𝒙 𝟑 + 5 𝒙 𝟕 + 8 or 𝟓 𝒙 𝟕 + 3 𝒙 𝟑 + 8 Standard Form: A polynomial arranged with terms having descending size of the exponents left to right.

6. Polynomials 8 𝑥 5 + 5 𝑥 4 −6 𝑥 3 − 2 𝑥 2 + 4 𝑥 1 - 10 Exponent
8 𝑥 𝑥 4 −6 𝑥 3 − 2 𝑥 𝑥
Exponent
Coefficient

7. Polynomial or Not?
1. Y = 3 𝑥 𝑥 1/3 + 6 Why not? 2. Y = 5 𝑏 𝑏 Why not? 3. Y = 8 𝑚 𝑚 𝑚 Why not?

8. Your Turn Is this a polynomial ? −5 𝑥 4 + 𝑥 5 − 3 𝑥 2 + 2𝑥 −3
−5 𝑥 𝑥 5 − 3 𝑥 𝑥 −3
Is this a polynomial?
If it is, what is the degree of the polynomial?
What is the lead coefficient?

9. Simplify Polynomials

10. Distributive property
EXAMPLE 1
Simplify by combining like terms
8x + 3x
= (8 + 3)x
Distributive property
= 11x
Add coefficients.
5p2 + p – 2p2
= (5p2 – 2p2) + p
Group like terms.
= 3p2 + p
Combine like terms.
3(y + 2) – 4(y – 7)
= 3y + 6 – 4y + 28
Distributive property
= (3y – 4y) + (6 + 28)
Group like terms.
= –y + 34
Combine like terms.

11. Group like terms. Combine like terms. EXAMPLE 1
Simplify by combining like terms
2x – 3y – 9x + y
= (2x – 9x) + (– 3y + y)
Group like terms.
= –7x – 2y
Combine like terms.

12. State the problem. Group like terms. Combine like terms.
GUIDED PRACTICE
for Example 1
8. Identify the terms, coefficients, like terms, and constant terms in the expression 2 + 5x – 6x2 + 7x – 3. Then simplify the expression.
SOLUTION
Terms:
2, 5x, –6x2 , 7x, –3
Coefficients:
5 from 5x, –6 from –6x2 , 7 from 7x
Like terms:
5x and 7x, 2 and –3
Constants:
2 and –3
Simplify:
2 + 5x –6x2 + 7x – 3
State the problem.
= –6x2 + 5x + 7x – 3 + 2
Group like terms.
= –6x2 +12x – 1
Combine like terms.

13. Combine like terms. Group like terms. Combine like terms.
GUIDED PRACTICE
for Example 1
Simplify the expression.
15m – 9m
SOLUTION
15m – 9m
= 6m
Combine like terms.
2n – 1 + 6n + 5
SOLUTION
2n – 1 + 6n + 5
= 2n + 6n + 5 – 1
Group like terms.
= 8n + 4
Combine like terms.

14. Group like terms. Combine like terms. Group like terms.
GUIDED PRACTICE
for Example 1
3p3 + 5p2 – p3
SOLUTION
3p3 + 5p2 – p3
= 3p3 – p3 + 5p2
Group like terms.
= 2p3 + 5p3
Combine like terms.
2q2 + q – 7q – 5q2
SOLUTION
2q2 + q – 7q – 5q2
= 2q2 – 5q2 – 7q + q
Group like terms.
= –3q2 – 6q
Combine like terms.

15. Distributive property
GUIDED PRACTICE
for Example 1
8(x – 3) – 2(x + 6)
SOLUTION
8(x – 3) – 2(x + 6)
= 8x – 24 – 2x – 12
Distributive property
= 8x – 2x – 24 – 12
Group like terms.
= 6x – 36
Combine like terms.
–4y – x + 10x + y
SOLUTION
–4y – x + 10x + y
= –4y + y – x + 10x
Group like terms.
= 9x –3y
Combine like terms.

16. Evaluate

17. Substitute –3 for x. Evaluate power. Multiply. Add. EXAMPLE 1
Evaluate an algebraic expression
Evaluate –4x2 –6x + 11 when x = –3.
–4x2 –6x + 11
= –4(–3)2 –6(–3) + 11
Substitute –3 for x.
= –4(9) –6(–3) + 11
Evaluate power.
= –
Multiply.
= –7
Add.

18. 1 2 Substitute 6 for x. Multiply. GUIDED PRACTICE for Examples 1 (–2)6
SOLUTION
(–2)6
= (–2) (–2) (–2) (–2) (–2) (–2)
= 64
5x(x – 2) when x = 6 2
SOLUTION
5x(x – 2)
= 5(6) (6 – 2)
Substitute 6 for x.
= 30 (4)
Multiply.
= 120

19. 3. Substitute –2 for y. Multiply. GUIDED PRACTICE for Examples 1
3y2 – 4y when y = – 2 3.
SOLUTION
3y2 – 4y
= 3(–2)2 – 4(–2)
Substitute –2 for y.
= 3(4) + 8
Multiply.
= 20