Adding and Subtracting
Polynomials
Simplify each expression.
ALGEBRA 1 LESSON 9-1
(For help, go to Lesson 1-7.)
1. 6t + 13t
2. 5g + 34g
3. 7k – 15k
4. 2b – 6 + 9b
5. 4n2 – 7n2
6. 8x2 – x2
4-2
Adding and Subtracting
Polynomials
ALGEBRA 1 LESSON 9-1
Solutions
1. 6t + 13t = (6 + 13)t = 19t
2. 5g + 34g = (5 + 34)g = 39g
3. 7k – 15k = (7 – 15)k = –8k
4. 2b – 6 + 9b = (2 + 9)b – 6 = 11b – 6
5. 4n2 – 7n2 = (4 – 7)n2 = –3n2
6. 8x2 – x2 = (8 – 1)x2 = 7x2
4-2
Adding and Subtracting
Polynomials
Find the degree of each monomial.
ALGEBRA 1 LESSON 9-1
a. 18
Degree: 0
The degree of a nonzero constant is 0.
b. 3xy3
Degree: 4
The exponents are 1 and 3. Their sum is 4.
c. 6c
Degree: 1
6c = 6c1. The exponent is 1.
4-2
Adding and Subtracting
Polynomials
Write each polynomial in standard form. Then name each
ALGEBRA 1 LESSON 9-1
polynomial by its degree and the number of its terms.
a. –2 + 7x
7x – 2
Place terms in order.
linear binomial
b. 3x5 – 2 – 2x5 + 7x
3x5 – 2x5 + 7x – 2
Place terms in order.
x5 + 7x – 2
Combine like terms.
fifth degree trinomial
4-2
Adding and Subtracting
Polynomials
Simplify (6x + 3x + 7) + (2x – 6x – 4).
ALGEBRA 1 LESSON 9-1
2
2
Method 1: Add vertically.
Line up like terms. Then add the coefficients.
6x2 + 3x + 7
2x2 – 6x – 4
8x2 – 3x + 3
Method 2: Add horizontally.
Group like terms. Then add the coefficients.
(6x2 + 3x + 7) + (2x2 – 6x – 4) = (6x2 + 2x2) + (3x – 6x) + (7 – 4)
= 8x2 – 3x + 3
4-2
Adding and Subtracting
Polynomials
Simplify (2x + 4x – 6) – (5x + 2x – 2).
ALGEBRA 1 LESSON 9-1
3
2
3
Method 1: Subtract vertically.
Line up like terms. Then add the coefficients.
(2x3 + 4x2
–(5x3
– 2x
– 6)
– 2)
Line up like terms.
2x3 + 4x2
–5x3
– 2x
–3x3 + 4x2 – 2x
–6
+2
–4
Add the opposite.
4-2
Adding and Subtracting
Polynomials
ALGEBRA 1 LESSON 9-1
(continued)
Method 2: Subtract horizontally.
(2x3 + 4x2 – 6) – (5x3 + 2x – 2)
= 2x3 + 4x2 – 6 – 5x3 – 2x + 2
Write the opposite of each term in
the polynomial being subtracted.
= (2x3 – 5x3) + 4x2 – 2x + (–6 + 2)
Group like terms.
= –3x3 + 4x2 – 2x – 4
Simplify.
4-2
Adding and Subtracting
Polynomials
Simplify each expression.
Then name each polynomial by its degree
ALGEBRA 1 LESSON 9-1
and number of terms.
1. –4 + 3x – 2x2
–2x2 + 3x – 4; quadratic trinomial
2. 2b2 – 4b3 + 6
–4b3 + 2b2 + 6; cubic trinomial
3. (2x4 + 3x – 4) + (–3x + 4 + x4)
3x4; fourth degree monomial
4. (–3r + 4r2 – 3) – (4r2 + 6r – 2)
–9r – 1; linear binomial
4-2