ObjectivesThe student will be able to:

LEARN ABOUT EXPONENTS AND ADD AND SUBTRACT POLYNOMIALS

MATH 8A

Rule: For all numbers x and all integers m and n ,

 SO,

EXAMPLES

PRACTICE

MORE EXAMPLES

What does each prefix mean?mono

one

bi

two

tri

three

What about poly?one or more

A polynomial is a monomial or a sum/difference of monomials.

Remember, an expression is not a polynomial if there is a variable in the denominator.

State whether each expression is a polynomial. If it is, identify it.

1) 7y - 3x + 4

trinomial

2) 10x3yz2

monomial

3) 5/2y2 + 7y

not a polynomial

The degree of a monomial is the sum of the exponents of the

variables.Find the degree of each monomial.

1) 5x2

2) 4a4b3c

3) -3

To find the degree of a polynomial, find the largest degree of the terms.

1) 8x2 - 2x + 7

Degrees: 2 1 0

Which is biggest? 2!

2) y7 + 6y4 + 3x4m4

Degrees: 7 4 8

8 is the degree!

A polynomial is normally put in ascending or descending order.

What is ascending order?

Going from small to big exponents.

What is descending order?

Going from big to small exponents.

Put in descending order:1) 8x - 3x2 + x4 - 4

x4 - 3x2 + 8x - 4

2) Put in descending order in terms of x:

12x2y3 - 6x3y2 + 3y - 2x

-6x3y2 + 12x2y3 - 2x + 3y

3) Put in ascending order in terms of y:

12x2y3 - 6x3y2 + 3y - 2x-2x + 3y -6x3y2 + 12x2y3

4) Put in ascending order:5a3 - 3 + 2a - a2

-3 + 2a - a2 + 5a3

1. Add the following polynomials:(9y - 7x + 15a) + (-3y + 8x - 8a)

Group your like terms.

9y - 3y - 7x + 8x + 15a - 8a

6y + x + 7a

Group your like terms.

3a2 + 3ab + 4ab - b2 + 6b2

3a2 + 7ab + 5b2

2. Add the following polynomials:(3a2 + 3ab - b2) + (4ab + 6b2)

Line up your like terms. 4x2 - 2xy + 3y2

+ -3x2 - xy + 2y2

_________________________

x2 - 3xy + 5y2

3. Add the following polynomials using column form:

(4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)

Rewrite subtraction as adding the opposite.

(9y - 7x + 15a) + (+ 3y - 8x + 8a)

Group the like terms.

9y + 3y - 7x - 8x + 15a + 8a

12y - 15x + 23a

4. Subtract the following polynomials:(9y - 7x + 15a) - (-3y + 8x - 8a)

Rewrite subtraction as adding the opposite.

(7a - 10b) + (- 3a - 4b)Group the like terms.

7a - 3a - 10b - 4b4a - 14b

5. Subtract the following polynomials:(7a - 10b) - (3a + 4b)

Line up your like terms and add the opposite.

4x2 - 2xy + 3y2

+ (+ 3x2 + xy - 2y2)--------------------------------------

7x2 - xy + y2

6. Subtract the following polynomials using column form:

(4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2)

PRACTICE

PRACTICE

PRACTICE