Studied by 50 people

0.0(0)

get a hint

hint

1

Variable

a symbol that represents (stands for) a number

Example: x or y

New cards

2

Coefficient

a number in front of a variable

Example: 3x, the 3 is the coefficient

New cards

3

Constant

a number with no variable attached

Example: 4, or in (w + 5), the 5 is a constant

New cards

4

Terms

variables, numbers, or the product of a number and variable(s) separated by addition or subtraction signs

Example: One Term: x or 4y Two Terms: 3z + 2 Three Terms: 8w - 7t + 9

New cards

5

Algebraic Expression

A mathematical phrase that can contain numbers, variables and operations(+,-,x,÷)

Examples: a + 1 or a - b or 3x

New cards

6

Base

a number or variable with an exponent on it

New cards

7

Like Terms

Like Terms have the same variable base and exponent example: 3x and 6x

New cards

8

How to: Combine Like Terms

add the coefficients & keep the variables the same (do not + or - exponents) The sign in front of each term is part of the term

4y² + 7y² = 11y² You can't add 3x + 6x²

New cards

9

Distributive Property (with variables)

a(b+c) = a(b) + a(c) Always distribute before combining like terms

Example:

6(2+4x) =

6(2) + 6(4x) =

12 + 24x

New cards

10

Monomial

One Term Example: 3x

New cards

11

Binomial

Two terms or monomials, connected through addition or subtraction Example: 3x - 6

New cards

12

Trinomial

Three terms or monomials, connected through addition or subtraction

Example: 3x² - 6x + 4

New cards

13

Polynomial

an expression that is a monomial, binomial, trinomial, or larger

New cards

14

Adding Polynomials

Just like combining like terms Example:

(3x² + 2x + 9)

(4x² + 6x - 1)

= (7x² + 8x + 8)

New cards

15

Subtracting Polynomials

1 - Rewrite 1st polynomial

2 - Change subtraction to addition

3 - Change the signs of EVERY term in the 2nd polynomial

4 - Combine like terms

(3x + 2xy + 7) - (6x - 4xy + 3)

(3x + 2xy + 7) + (-6x + 4xy - 3)

= -3x + 6xy + 4

New cards

16

To Find: Greatest Common Factor (GCF)

Method 1

Completely factor each number (list all the factors)

The largest number they have in common is the answer

New cards

17

To Find: Greatest Common Factor (GCF)

Method 2

Divide the numbers by any common factor

Check to see if the quotients can be divided by another common factor

Continue to divide by common factors until the only common factor is 1

The GCF will be the product of all the divisors (the common factors you divided by)

New cards

18

Use GCF to Factor Linear Expressions

6x + 18

Find the GCF of the coefficient & the constant GCF of 6 & 18 is 6

Divide the original problem by the GCF to get the second factor

(6x+18) / 6

= x + 3

Write your answer as the product of the GCF & the Quotient 6(x + 3)

New cards

19

Using GCF to Factor Linear Expressions with Fractions

Use Rules for Using GCF to Factor Linear Expressions ***Differences:

change mixed numbers to improper fractions

need common denominators

find the GCF of the fractions (the gcf of the numerators over the common denominator)

LOOK BACK AT YOUR NOTES, THIS IS TOUGH

New cards