Section 9-1 Adding and Subtracting PolynomialsSPI 12C: add and subtract algebraic expressions

Objectives:• Classify a polynomial by degree and number of terms.• Simplify polynomials by adding and subtracting like terms.• Write polynomials in standard form.

Polynomial: sum or difference of 2 or more monomials.Monomial: one termBinomial: two terms (separated by a + or – sign)Trinomial: three terms (separated by a + or – sign)

Degree of a monomial (one term): sum of the exponents of its variables EX: 4m3n2 (degree 5); 4x2 (degree 2)

Degree of a polynomial (more than one term): the degree of the monomial with the greatest exponent. EX: 4x2 + 2x + 3 (degree is 2)

Naming Polynomials

• Always write polynomials in standard form: - degrees of terms decrease from left to right

• Degree of polynomial is the monomial with the greatest exponent

• Name Polynomials based of degree and number of monomials

How would you name the polynomial 3x4 + 5x2 – 1?

Fourth degree trinomial

3x4 + 5x2 – 1

Find the degree of each monomial.

a. 18

b. 3xy3

c. 6c

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

The exponents are 1 and 3. Degree: 4

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

Write the polynomial in standard form. Then name the

polynomial by its degree and the number of its terms.

–2 + 7x

linear binomial

Place terms in order.7x – 2

Naming Polynomials

Adding and Subtracting Polynomials

3x2 and x2 are like terms

3x2 and x are NOT like terms

Negative sign outside parenthesis: • distribute negative sign to each term on the inside of the parenthesis

– (5x2 + 2x – 2) = – 5x2 – 2x + 2

Combining Like Terms

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) =

= 8x2 – 3x + 3

Adding and Subtracting Polynomials

Two Methods• Vertical method• Horizontal method

(6x2 + 2x2) + (3x – 6x) + (7 – 4)

Simplify (2x3 + 4x2 – 6) – (5x3 + 2x – 2).

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

Adding and Subtracting Polynomials

Method 2: Subtract horizontally

= 2x3 + 4x2 – 6 – 5x3 – 2x + 2 Distribute negative

= (2x3 – 5x3) + (4x2 – 2x) + (–6 + 2) Group like terms.

= –3x3 + 4x2 – 2x – 4 Simplify

(2x3 + 4x2 – 6) – (5x3 + 2x – 2)

Adding and Subtracting Polynomials