1097 Math/Algebra 1-1

A number expressed using letters and/or numerals.

algebraic expression

Any one factor or product of factors in a given term is the _______________ of the rest of the term.

coefficient

A numeral in an algebraic expression used to represent a value which does not change.

constant

Small numeral written at the upper right of a base to show how many times the base is used as a factor.

exponent or power

Any of the elements, quantities, or symbols that produce a given product when multiplied together.

factor

A numeral or letter written above and to the left of the radical sign to indicate the required root.

index of a radical

Terms that have the same variables and the same exponents for corresponding variables.

like terms

A polynomial with exactly one term.

monomial

Placed over an expression to denote that a root is to be found.

radical sign

The quantity under a radical sign.

radicand

For a given number, one of two equal factors whose product is that number.

square root

An algebraic expression consisting of a single numeral or letter, or the product or quotient of numerals and/or letters.

terms

A symbol, usually a letter, used to represent an unknown value in a given algebraic expression.

Variable

In algebra, subtraction is performed in the same manner as addition. The only difference is that the sign of the ________________ must be changed.

subtrahend

The subtrahend is the ________________ number in a subtraction equation.

second (the number being taken from another number.)

The first number in a subtraction problem is the ________________.

minuend

To perform algebraic subtraction, change the sign of the subtrahend and?

combine as in addition, (Subtract 3 from 7, 7-3= 7+(-3)=4)

In algebra if the signs are alike, ___________the absolute value of the numbers and attach their common sign to the sum.

add

To add numbers with opposite signs, _____________ the smaller absolute value from the greater absolute value and attach the sign of the greater to the result.

subtract

When adding more than two numbers, first combine all the positive numbers to obtain one positive value. Then combine all the negative numbers to obtain one negative value. Finally, proceed as before, subtract the smaller absolute value from the greater absolute value and attach the sign of the __________ to the value.

greater

When multiplying two numbers with the same sign (whether both positive or both negative), the product is always?

positive

When multipying two number with opposite signs (one negative number and one positive), the product is always?

negative

When the divisor and the dividend have the same sign, (both positive or both negative), the quotient is?

positive

When the divisor and dividend have opposite signs (one negative and one positive), the quotient is ?

negative

When the divisor and the dividend have the same sign, (both positive or both negative), the quotient is?

Positive

When the divisor and dividend have opposite signs (one negative and one positive), the quotient is ?

Negative

In an algebraic expression, the order in which terms are combined is very important. What are the rules in order?

a) Simplify expressions within parentheses.

b) Combine from left to right all terms to be multiplied or divided.

c) Combine from left to right

In an algebraic expression 4x+3y, the numbers 4 and 3 represent definite numbers and are therefore referred to as ___________, and the letters x and y represent unknown numbers which we call __________.

Constants/variables

The process of evaluating an algebraic expression is two steps.

1) Assign each variable a numerical value.

A=1, b=2, c=3

2) Simplify

3a+4b+c

3(1)+4(2)+3=14

Evaluation of expressions involving fractions, exponents, and radicals follows the same steps.

a) Assign each variable

b) Simplify the expression

Rules for adding positive numbers, if the signs of the numbers are alike, add the absolute value of the numbers and attach their ___________ to the sum.

common sign

To add numbers with opposite signs, subtract the _________ absolute value from the _____________ absolute value, and attach the sign of the greater to the result.

Smaller/greater

When adding numbers with the same sign, add their absolute values and attach their ___________ sign to the sum.

Common (subtract -18 from -78, -78-(-18)= -78+(+18)=-60) Remember: To perform algebraic subtraction, change the sign of the subtrahend and combine as in addition.

When multiplying two number with the same sign (whether both positive or both negative), the product is always ___________.

Positive

When multiplying two numbers with opposite signs (one negative and one positive), the product is always?

negative

When dividing and the divisor and dividend have the same sign (both positive or negative), the quotient is?

Positive

When dividing and the divisor and dividend have opposite signs (one positive and one negative), the quotient is?

Negative

Write a polynomial in _______________ powers of one variable.

descending

An algebraic expression with one or more terms.

Polynomial

Any nonzero quantity raised to the _______ power has a value of 1

Zero example 7 x(to the power of 0)=7(1)=7

A polynomial with exactly one term is called a?

Monomial example 2xy

A polynomial consisting of the sum or difference of exactly two terms.

Binomial 3x+4x

A polynomial consisting of the sum or difference of exactly three terms.

Trinomial 2x+3xy-y

In order for terms to be like terms, the terms must have the same ___________ and the same ______________ for corresponding variables.

Variables/exponents

Terms which are not like terms _____________ be added or subtracted.

cannot

When adding like terms with the same sign, add their numerical coefficients and ___________ the variables common to the terms

Attach (-6y+(-4y)=-10y)

When adding like terms with opposite signs, _________ the coefficient with the smaller absolute value from the coefficient with the greater absolute value.

subtract

The sign of the result is the same as the sign of the ______________ with the greater absolute value.

Coefficient (-4ab + 2ab = -2ab)

To subtract like terms, change the sign of the ______________ and then proceed as in addition.

subtrahend

When like terms are found within a given polynomial, they can be ___________ to form one term. This procedure helps to simplify the given polynomial.

Combined (2x+2x-3y-2y=4x-5y)

Sometimes the terms of a polynomial will need to be ______________ in order to make combining easier.

Rearranged (3a+2b-a+3b= 3a-a+2b+3b= 2b+5b)

Be careful of the "+" and "-" signs when rearranging the ___________.

terms

Polynomials should be written in ______________ powers of one of the variables.

descending

When the exponent of "x" is 1, we simply write x. When the exponent of "x" is o, we write no _______________ because any nonzero value raised tot he zero power equals 1.

variable

Since terms are usually written with the ____________ in alphabetical order, it is best to express a polynomial in descending powers of the first variable.

variables

To multiply monomials, two steps

a) Multiply the numerical coefficients. (Be careful to apply the correct sign to the product)

b) Multiply the variables

To multiply variables, _______ their exponents.

add

When no exponent is written, the exponent is?

1

Division of monomials is two steps.

a) Divide the numerical coefficients. (apply the correct sign to the quotient)

b) Divide the variables

To divide variables, _________ the smaller exponent from the greater exponent.

subtract

Any nonzero power raised to the zero power equals?

1

A fraction can be reduced (simplified) by __________ the numerator and denominator by the greatest common factor.

dividing

Algebraic fractions can be simplified using 2 steps.

a) Divide numerical coefficients. (Apply the correct sign)

b) Divide the variables (subtract the smaller exponent from the greater exponent)

The negative sign is placed in ________ of the fraction rather than in the numerator or denominator.

front

When simplifying fractions involving variables, subtract the smaller exponent from the greater exponent. Place the resulting variable in the same _________ (numerator or denominator) as the variable with the greater exponent.

position