PolynomialsEssential Question:How do you add or subtract polynomials?

Polynomials• Polynomial

– A monomial, or a sum or difference of monomials• Degree

– The degree of a polynomial in one variable is determined by the exponent with the greatest value within the polynomial

– Highest exponent within the polynomial• Standard Form

– The terms of a polynomial are ordered from left to right in decreasing order.

Naming a Polynomial According to Degree

• Linear – if the degree is 1

• Quadratic – if the degree is 2

• Cubic – if the degree is 3

• 4th Degree –if the degree is 4

• 5th Degree– if the degree is 5

Write in standard form then identify the degree of the polynomial.1. 9 + x – 4x2

-4x2 + x + 9degree: quadratic

2. X + 3x3 – 23x3 + x – 2degree: cubic

3. 15 + 2x – 3x2

-3x2 + 2x + 15degree: quadratic

4. 3x4 + 23 – 2x + 2x3

3x4 + 2x3 – 2x + 23degree: quartic

5. 3 + zz + 3degree: linear

Classifying Polynomials according to number of terms.

• Terms –it is a basic unit in a polynomial

including the sign.–separated by + or –

• Types:Monomial – one term (no + or – in between)Binomial – polynomial with two termsTrinomial – polynomial with three terms

Classify according to number of terms.1. 2x2 – 5x + 2

2. -5x + 5

3. 7x3 + 10x – 2xy

4. -10x3yz

5. -xy + 3y

trinomial

binomial

trinomial

binomial

monomial

Rules in Adding Polynomials

1. Arrange each polynomial in standard form.

2. Write the terms that are similar in only one column.

3. Add only the coefficients.4. Do not add the exponents. Copy as it is.

Adding Polynomials

• Find the sum of (2x2 – 3x + 5) + (4x2 + 7x – 2)

Solution:2x2 – 3x + 5

+ 4x2 + 7x – 26x2 + 4x+ 3

The sum is 6x2 + 4x + 3.

Find the sum of (3x2 + 4x4 – x + 1) + (3x4 + x2 – 6)

Solution:4x4 + 3x2 – x + 1

+ 3x4 + x2 – 6 + 4x2 – x – 5

The sum is 7x4 + 4x2 – x – 5.

7x4

Do this…Find the sum of each of the following. Make

sure to write first in standard form.

1. (4x4 + x3 – 6) + (x3 + x2)

2. (2y3 + y2 + 1) + (3y3 – y2 + 2)

3. (2c – 3) + (c2 + c + 4)

4. (3d2 + 7d – 6) + (d3 + d2 – d – 1)

5. (4x2 – 7x3 + 2x – 3) + (5x3 – 3x – 4x2 + 6)

Write a polynomial expression for the perimeter of each polygon.1.

2. 3.

x2 + x

2x2

x2 + x

2x2

a + 1a3 + 2a

2a3 + a + 3

2x – 3 2x – 3

3x2 + 2 3x2 + 2

2x2 + x + 1

Rules in Subtracting Polynomials

1. Arrange in standard Form2. Write in only one column those that are

similar terms.3. Apply “Keep-Change-Change”4. Proceed to addition.

Subtracting Polynomials

Find the difference of(3x2 – 2x + 8) – (x2 – 4)

Solution:3x2 – 2x + 8

– x2 – 4 + - +2x2 – 2x + 12

The difference is 2x2 – 2x + 12.

Subtract: (4x2 + 2 + 3x) – (3x – 2x2 + 7)

Solution:

4x2 + 3x + 2– -2x2 + 3x + 7+ + – –

6x2 + 0x – 5

The difference is 6x2 – 5.

Do this…Find the difference of each of the following

polynomials.

1. (12x2 + 5x + 11) – (10x2 + 3x + 2)

2. (3x4 + 2x2 ) – (2x4 + 3)

3. (x3 + x2 + 7) – (x2 + x )

4. (3x2 + 3 – 5x) – (–x – 4 + 2x2)

5. (4y2 – y + 6) – (3y – 2)