## ALBEBRA EXPRESSION

Term Definition
algebraic expression Is a mathematical phrase that's a combination of one or more variables, constants , and operation symbols. A subtraction or addition operation sign between monomials is considered part of the term on the term on the right. 25q+10d+5n
coefficient When you see a number and a letter together, indicating multiplication, the number is called the ________ of the variable
constant Is a quantity that stays the same, like the number of cents in a dollar.
variable Is a quantity that can change like the cost of a carton of orange juice or a piece of data in a formula.
monomial Is an expression in which variables and constants may stand alone or be multiplied., examples 8, X^2, 2X^2, 4a/3. Monomials can be combined by addition or subtraction into larger expressions called binomials and multinomials or polynomials.
multinomial or polynomial Is a monomial or a sum of monomials.
like terms terms that have the same varible raised to the same power, 6x^3 and 3X^3.
simplifying combine like terms or use properties to make polynomial expressions easier to work with. Use the distributive property to get rid of any parenthesis.
types of polynomials 4 types,
monomial – 1 term
binomial – 2 terms, 5x+3
trinomial – 3 terms, 1/2^2-5x+11, sum of monomials
other polynomials
using properties to simplify expressions it may be easier to work with subtracted terms if you make them into added terms. Subtracting +n is the same as adding – n and subtracting -n is the same as adding +n.
distributive property States that for any numbers a, b, c:
a(b+c) = (ab) + (ac)
a(b-c) = (ab) – (ac)
adding and subtracting with roots When adding or subtracting roots of any given number, treat them as you do variables. If they are the same or can be made the same by factoring, you can combine terms by adding or subtracting
adding roots When the roots are the same, use the distributive property. (pg. 106)
subtracting roots When the roots are not the same try to simplify so that they are. If you can't, do not try to compute unless you are estimating the roots.
rational number Is a number that can be represented by a ratio of two integers where the denominator does not equal zero.
irrational number Is a number that cannot be represented by a ratio of two integers. It can be approximated on the number line as a decimal.
imaginary number Is a number that is the square root of a negative real number.
absolute value The distance the number is from zero. The distance the number from zero can not be negative.
factorial Take any whole number and call it n. Multiply all the positive integers from 1 through n. The product is call n factorial n!
rational number Is a number that can be represented by a ratio of two integers where the denominator does not equal zero.
irrational number Is a number that cannot be represented by a ratio of two integers. It can be approximated on the number line as a decimal.
imaginary number Is a number that is the square root of a negative real number.
absolute value The distance the number is from zero. The distance the number from zero can not be negative.
factorial Take any whole number and call it n. Multiply all the positive integers from 1 through n. The product is call n factorial n!
making division distributive First write the division problem as a multiplication problem, then use the distributive property.
(b+c) / a = (b+c) * 1/a. To rewrite the division as a multiplication, use reciprocals. Example 6/2 has the same result as 6/2 = 6*1/2.
identity element Is a number that combines with another number without changing its value. For addition the identify element is zero. For multiplication the identity number is one.
additive inverse The sum is always zero. Additive inverses are also called opposites.
multiplicative inverse The product is always one. Multiplicative inverse is usually called reciprocals. Zero is the only number with no multiplicative inverse.
perfect powers Any number that is a product of repeated whole number factors is a perfect power.
irrational roots A whole number that is not a perfect square. That means that the square root cannot be represented by a ration of integers. It is represented by a non-repeating, non-terminating decimal.
square root When you look for a number that when multiplied by itself to get the product is called the square root. The square root can be negative. Remember a negative times a negative equals a positive.