Adding and Subtracting Polynomials

ALGEBRA 1 LESSON 9-1ALGEBRA 1 LESSON 9-1

(For help, go to Lesson 1-7.)

Simplify each expression.

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 9-1ALGEBRA 1 LESSON 9-1

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

Solutions

4-2

ALGEBRA 1 LESSON 9-1ALGEBRA 1 LESSON 9-1Adding and Subtracting Polynomials

Find the degree of each monomial.

a. 18

b. 3xy3

c. 6c

4-2

The degree of a nonzero constant is 0.Degree: 0

The exponents are 1 and 3. Their sum is 4.Degree: 4

6c = 6c1. The exponent is 1.Degree: 1

Adding and Subtracting Polynomials

ALGEBRA 1 LESSON 9-1ALGEBRA 1 LESSON 9-1

Write each polynomial in standard form. Then name each

polynomial by its degree and the number of its terms.

a. –2 + 7x

linear binomial

b. 3x5 – 2 – 2x5 + 7x

x5 + 7x – 2 Combine like terms.

fifth degree trinomial

Place terms in order.3x5 – 2x5 + 7x – 2

Place terms in order.7x – 2

4-2

Adding and Subtracting Polynomials

ALGEBRA 1 LESSON 9-1ALGEBRA 1 LESSON 9-1

Simplify (6x2 + 3x + 7) + (2x2 – 6x – 4).

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 (2x3 + 4x2 – 6) – (5x3 + 2x – 2).

ALGEBRA 1 LESSON 9-1ALGEBRA 1 LESSON 9-1

Method 1: Subtract vertically.

Line up like terms. Then add the coefficients.

(2x3 + 4x2 – 6) Line up like terms.

–(5x3 – 2x – 2)

2x3 + 4x2 – 6 Add the opposite.

–5x3 – 2x + 2

–3x3 + 4x2 – 2x – 4

4-2

Adding and Subtracting Polynomials

(continued)

ALGEBRA 1 LESSON 9-1ALGEBRA 1 LESSON 9-1

Method 2: Subtract horizontally.

= 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.

(2x3 + 4x2 – 6) – (5x3 + 2x – 2)

4-2

Adding and Subtracting Polynomials

ALGEBRA 1 LESSON 9-1ALGEBRA 1 LESSON 9-1

Simplify each expression. Then name each polynomial by its degree and number of terms.

1. –4 + 3x – 2x2

2. 2b2 – 4b3 + 6

3. (2x4 + 3x – 4) + (–3x + 4 + x4)

4. (–3r + 4r2 – 3) – (4r2 + 6r – 2)

–2x2 + 3x – 4; quadratic trinomial

–4b3 + 2b2 + 6; cubic trinomial

3x4; fourth degree monomial

–9r – 1; linear binomial

4-2