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Notes 4-14
Algebra I Pre-AP
Section 7.6
Adding and Subtracting Polynomials
Name __________________________________
Review: Match the following polynomial functions to their corresponding names.
1.
2.
3.
4.
5.
6.
7.
______ y = x3 + 2
______ f(x) = 4x2
______ f(x) = 7x – 2
______ y = 9
______ f(x) = 6x4 + 7
______ y = 5x3 + 2x – 3
______ y = 3x3 + 2x2 – 3x + 2
A.
B.
C.
D.
E.
F.
G.
constant monomial
cubic trinomial
quadratic monomial
cubic four-term polynomial
cubic binomial
fourth degree binomial
linear binomial
To ADD or SUBTRACT polynomials, combine like terms.
1. 15m3 + 6m2 + 2m3
2. 3x2 + 5 – 7x2 + 12
3. 2x2 – x2y + 7x2y
Polynomials can be added in either vertical or horizontal form.
In vertical form, align the like terms.
5x2 + 4x + 1
+ 2x2 + 5x + 2
4b5 - 7b3 + b2 – 12
3b5 + 6b3 – 5b2 + 10
+ 9b5
+ 10b2 - 3
In horizontal form, use the Associative and Commutative
property to regroup and combine like terms.
( 5x2 + 4x + 1) + ( 2x2 + 5x + 2)
(4b5 - 7b3 + b2 – 12) + (3b5 + 6b3 – 5b2 + 10) + (9b5 + 10b2 – 3)
To SUBTRACT polynomials, distribute a –1 to each term in the polynomial you are subtracting.
(a4- 2a ) – (3a4 – 3a + 1)
Try These - Directions: Find each sum or difference. Then write in STANDARD form and CLASSIFY the
polynomial based on its degree and number of terms.
1. (x + 2x2) + (2x – 4x2)
2. (2m4 + 3m2 – m) + (m2 – 2m4)
3. (3x2 – 5x) – (x2 + 4x + 3)
4. (3y3 – 11y + 3) – (5y3 + y2 + 2)
5. (2a3 + 3a2 + 7a) + (a3 + a2 – 2a)
6. (x2 – 6) + (5x2 + x – 3)
7. (5m3 + 2m2 + 2) – (m3 + 3m2 – 2)
8. (2x2 + 9x – 17) + (x2 – 6x – 3)