1. Adding & Subtracting Polynomials
Mrs. Book
Liberty Hill Middle School
Algebra I

2. Bellwork Simplify each expression 6t + 13t 5g + 34g 7k – 15k
2b – 6 + 9b
4n2 – 7n2
8x2 – x2
19t, 39g, -8k, 11b – 6, -3n2, 7x2

3. Vocabulary
Monomial – an expression that is a number, a variable, or a product of a number and one or more variables.
Examples: y x2y
Degree of a monomial is the sum of the exponents of its variables. For a nonzero constant, the degree is 0. Zero has no degree.
Examples:
⅔x Degree: 1 ⅔x = ⅔x1. The exponent is 1.
7x2y3 Degree: 5 The exponents are 2 and 3. Their sum is 5.

4. Vocabulary 3x4 + 5x2 – 7x + 1 Degree: 4 2 1 0
Polynomial – is a monomial or the sum or difference of two or more monomials.
3x4 + 5x2 – 7x + 1
Degree:
Standard form of a polynomial means that the degrees of its monomial terms decrease from left to right.
The degree of a polynomial in one variable is the same as the degree of the monomial with the greatest exponent.
The degree of 3x4 + 5x2 – 7x + 1 is 4.

5. Classifying Polynomials

6. Practice Classifying Polynomials
Write each polynomial in standard form. Then name each polynomial based on its degree and the number of its terms.
6x2 + 7 – 9x4
3y – 4 – y3
8 + 7v – 11v
-9x4 + 6x2 + 7: degree 4 trinomial
-y3 + 3y – 4: cubic trinomial
-4v + 8: linear binomial

7. Adding Polynomials Simplify (4x2 + 6x + 7) + (2x2 – 9x + 1)
Method 1: Add vertically
Line up like terms. Then add the coefficients.
4x2 + 6x + 7
+ 2x2 – 9x + 1
6x2 – 3x + 8

8. Adding Polynomials Simplify (4x2 + 6x + 7) + (2x2 – 9x + 1)
Method 2: Add horizontally
Group like terms. Then add the coefficients.
(4x2 + 6x + 7) + (2x2 – 9x + 1)
(4x2 + 2x2) + (6x – 9x) + (7 + 1)
= 6x2 – 3x + 8

9. Practice Adding Polynomials
Simplify each sum
(12m2 + 4) + (8m2 + 5)
(t2 – 6) + (3t2 + 11)
(2p3 + 6p2 + 10p) + (9p3 + 11p2 + 3p)
20m2 + 9
4t2 + 5
11p3 + 17p2 + 13p

10. Subtract Polynomials Simplify (2x3 + 5x2 – 3x) – (x3 – 8x2 + 11)
Method 1: Subtract vertically
Line up like terms. Then add the opposite of each term in the polynomial being subtracted.
2x3 + 5x2 – 3x
- (x3 – 8x )
x3 + 13x2 – 3x – 11

11. Subtracting Polynomials
Simplify (2x3 + 5x2 – 3x) – (x3 – 8x2 + 11)
Method 2: Subtract horizontally
Change the signs of all terms in the polynomial being subtracted. Group like terms. Then simplify.
(2x3 + 5x2 – 3x) – (x3 – 8x2 + 11)
2x3 + 5x2 – 3x – x3 + 8x2 - 11
(2x3 – x3) + (5x2 + 8x2) + -3x - 11
= x3 +13x2 – 3x – 11

12. Subtracting Polynomials
Simplify each difference:
(v3 + 6v2 – v) – (9v3 – 7v2 + 3v)
(30d3 – 29d2 – 3d) – (2d3 + d2)
(4x2 + 5x + 1) – (6x2 + x + 8)
-8v3 + 13v2 – 4v
28d3 – 30d2 – 3d
-2x2 + 4x - 7