2.1 Algebraic Expressions

Question 1

Quotient

Answer 1

Solution to a division problem

Question 2

Monomial or Terms

Answer 2

an algebraic expression consisting only one term

eg: 7x^3y^4, 3xyz^2

Question 3

Binomial

Answer 3

an algebraic expression consisting two terms

eg: 2x+4y 3x^4-4xyz^3

Question 4

Trinomial

Answer 4

an algebraic expression consisting three terms

eg: 3x^2-5x+2

Question 5

Multinomial

Answer 5

an algebraic expression consisting of more than one term

eg: 7x+6y+3x^3+6x^2y

Question 6

Coefficient

Answer 6

the number to the left of the variable

eg: -5x^3y^2 coefficient = -5

Question 7

Degree of monomial

Answer 7

sum of all the exponents in the term

eg: 4x^3y^2z = 3+2+1 (over z) = 6

therefore, degree for this is 6

Question 8

Degree of a Polynomial

Answer 8

the same as the term having the highest degree and non-zero coefficient

Eg: 7x^3y^2-4xz^5+2x^3y = Highest degree is 5 (in the four)

Question 9

Grouping

Answer 9

when parentheses are used to show that the terms contained in them are a single multinomial

eg: 5x^2-3x+y and 2x-3y = (5x^2-3x+y)+(2x-3y)

Question 10

Grouping removal is governed by the following laws:

if a plus sign…

Answer 10

1. if there is a + sign in between two groupings the “()” may be removed without affecting the functions

Question 11

Grouping removal is governed by the following laws:

if a subtraction sign…

Answer 11

2. if there is a - sign in between two groupings the “()” may be removed without affecting the functions or their + or negative signs

Question 12

Grouping removal is governed by the following laws:

if multiple grouping symbols are present…

Answer 12

inner ones are to be removed first:

eg: 2x- (4x^3- {3x^2-5y}) is changed into
2x- (4x^3- 3x^2-5y)

Question 13

Steps of Multiplying Algebraic Expressions:

Monomial to monomial

Answer 13

1. Multiply coefficients
2. Use to the rule for multiplying exponents and add the powers

Combine solution of the Coefficients and the combined exponent’s answer

Question 14

Steps of Multiplying Algebraic Expressions:

Polynomial to monomial

Answer 14

1. Use distributive property by multiplying the monomial by each polynomial section.
   eg. (5x^2y^4) ( 3xy-4x^3+2xy^2)
2. (5x^2y^4)(3xy)= 15x^3y^5 as part 1 of 3 for the solution.

the solution is the combination of each 1-3 parts of the polynomials multiplication answer.

Question 15

Steps of Multiplying Algebraic Expressions:

Polynomial to Polynomial

Answer 15

1. Align the polynomials in Descending order by the power of x:

eg: x^2-3x+9
- x+3
1. Multiply each exponent and coefficient by -x
2. Multiply each exponent and coefficient by 3

3. Take line 1 and 2 of multiplication results and add them together in relation to their powers

eg: x^2-3x+9
- x+3
1. -x^3+3x^2-9x
2. 3x^2-9x+27
3. Sum: -x^3+6x^2-18x+27

Question 16

Rules of Signs:

1. Add two numbers with like signs
2. Add two numbers with diff signs
3. A positive times a positive… negative time a negative
4. Mulitply or divide numbers with unlike signs (Neg x a Postive)

Answer 16

1. get the sum of them and use the sign that they both have either positive or negative
2. get the sum of them and use the sign of the number with a greater value
3. a Positive
4. a Negative

Question 17

Steps of Dividing Algebraic Expressions:

Monomial to monomial

Answer 17

1. Get quotient of coefficient and variables
2. Multiply solutions:

eg:

Question 18

Degree of a monomial

Answer 18

is the sum of the all the variables in the term.

Question 19

Degree of a constant

eg: 6,0,-sqrroot3

Answer 19

is 0

Question 20

Degree of a polynominal

Answer 20

is the highest sum of the all the variables in the term.

Question 21

When you multiply variables with the same base with exponents .. the exponents

Answer 21

add together