Math 105 notes leading up to midterm
Math 105 notes leading up to midterm MATH 105
Edinboro University of Pennsylvania
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This 3 page Class Notes was uploaded by Cassandra Notetaker on Sunday March 20, 2016. The Class Notes belongs to MATH 105 at Edinboro University of Pennsylvania taught by Dr. Phillip Funtulis in Spring 2016. Since its upload, it has received 9 views. For similar materials see College Algebra in Mathematics (M) at Edinboro University of Pennsylvania.
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Date Created: 03/20/16
Rational Expressions 2/15/16 Relatively Prime numbers that aren’t prime but their least common denominator is those two numbers multiplied together. Ex. 8 and 9. Prime Polynomial does not factor into polynomials of a smaller degree. To Add Fractions: 1. Find the least common denominator. 2. Multiply the denominator of each fraction to make the least common denominator. 3. Add the numerators. Fractions “Rule of Thumb” with variables in the denominator, the least common denominator is always the largest power. Rational Expressions “Rule of Thumb” If you can, factor out a nontrivial (not 1) greatest common factor first. Rational Expression P/Q, where P and Q are polynomials and Q ≠ 0; the numerator can be zero as long as the denominator isn’t. Domain set of all allowable values that we can plug in to get a denominator ≠ 0. Addition / Subtraction a/c + b/c = a+b/c Multiplication / Division a/c x b/d = a x b/ c x d m n mn Quotient Rule m > n, a / a = a Rational Exponent a = ( √a) , n ≠ 0 Index the superscript on the root symbol, indicates degree to which the root is taken. Ex. square root has an index of 2, cube root index of 3, etc. Radicand the value within the root symbol. **When faced with a negative exponent, make it positive** When Radicals are Simplified: 1. Radicand will have no factor raised to a power greater than or equal to the index. 2. The radicand has no fractions. 3. Exponents and indices are relatively prime (no common factors other than 1). 4. All operations have been performed. 5. Like terms in radicals have the same constant, same variable(s), and same power(s). 1 Linear Equations The inverse operation of multiplication is division. To isolate one variable in an expression, perform the inverse operation to move the other variables to the opposite side. Ex. I = Prt solved for r, r = I/Pt Variable Term includes the variable and coefficient. **dividing by a fraction is multiplying by the reciprocal** Literal Equation involve “variable” solutions. I = Prt I – interest amount, P – principle amount invested, r – rate, t – amount of time Modeling “realworld” situation expressed using math. 1. Read the word problem. 2. Assign a variable to the unknown value. What are we looking for? 3. Find an equation that can be used to solve for the unknown value. Zero Factor Property If a and b are complex numbers with ab = 0, then a = 0, b = 0, or both a and b = 0. Square Root Property a quadratic of form x = k can also be solved by factoring (difference of squares)