Bellwork

Simplify the following by combining like terms.

1. 2xyz + 4x + 5y + 2x – 3z – 2y – xyz

2. 3x2 + 4x3 – 2x + x3 – x2 + 2x

Unit 2 Algebra Investigations

Lesson 1: Exploring Algebraic Expressions and Equivalent

Expressions

Notes 2.1: Add and Subtract Polynomials

VocabularyMonomial

A number, variable, or the product of a number and one or more variables.

Polynomial

A monomial or the sum of monomials.Binomial

A polynomial with 2 terms.Trinomial

A polynomial with 3 terms.

Vocabulary

Degree

The greatest exponent in a polynomial.Standard Form

When a polynomial is written from largest exponent to smallest exponent.

Leading coefficient

The coefficient of the first term of a polynomial in standard form.

(Ex 1) Rewrite a polynomial

Write 7 + 2x4 – 4x so that the exponents decrease from left to right. Identify the degree and the leading coefficient of the polynomial.

Checkpoint: Write the polynomial so that the exponents decrease. Identify the degree and the leading coefficient.

1. 5x + 13 + 8x3

2. 4y4 – 7y5 + 2y

3. -5m2 + 1 – 9m

4. 2r3 + 4r4 + r – 5r2

(Ex 2) Add polynomials

Find the sum:

a) (4x3 + x2 – 5) + (7x + x3 – 3x2)

b) (x2 + x + 8) + (x2 – x – 1)

Checkpoint: Find the sum.

5. (3x4 – 2x2 – 1) + (5x3 – x2 + 9x4)

6. (4x2 – 15 + 6x3) + (8x + 24 + x2)

(Ex 3) Subtract polynomials

Find the difference:

a) (3x2 + 6x – 4) – (x2 – x – 7)

b) (4z2 – 3) – (-2z2 + 5z – 1)

Checkpoint: Find the difference.

7. (3t2 – 5t + t4) – (11t4 – 3t2)

8. (4p3 + 3p – 6) – (-2p3 – p2 + 3)