Whether you need a quick refresher on the subject, or are prepping for your next test, we think you’ll agree that REA’s *Super Review *provides all you need to know!

are (12, 0), (11, 1), (10, 2), (9, 3), (8, 4), (7, 5), (6, 6). But none of these satisfy r1 r2 = 8, so we cannot use B). To complete the square it is necessary to isolate the constant term, x2 − 12x = −8. Then take of the coefficient of the x term, square it and add to both sides Now we can use the previous method to factor the left side: r1 + r2 = 12, r1r2 = 36 is satisfied by the pair (6, 6), so we have: (x − 6) (x − 6) = (x − 6)2 = 28. Now take the square root of both sides and solve for

number of variations and the number of positive roots of the equation is an even number. The number of negative roots of f(x) = 0 cannot exceed the number of variations of sign of f(–x). The difference between the number of variations and the number of negative roots is an even number. Example: 3x5 – 4x4 + 3x3 – x + 1 = 0 has four variations in sign so the number of positive roots cannot exceed four. It can be 0, 2, or 4. f(–x) would be obtained as shown below: The number of variations equals

direction of this vector is given by an angle . Hence, we may express this complex number x + yi as the vector A ≤ α, where , and A ≤ a = x + yi. The complex number N = A(cos a + isin a) is said to be in trigonometric (or polar) form, whereas the complex number N = x + yi is said to be in rectangular form. 18.1 DeMoivre’s Theorem The nth power of A(cos nθ isin nθ) is given by: [A(cos θ + isin θ)]n = An (cos nθ + isin nθ). Problem Solving Examples: Write each of the following in the form a +

hold for certain subsets of the reals , such as the rationals . They do not hold for all subsets of , however; for instance, the integers do not contain multiplicative inverses for integers other than 1 or −1. Problem Solving Examples: Find the sum 8 + (−3). The sum of 8 + (−3) can be obtained by using facts from arithmetic and the associative law: Using the associative law of addition (a + b) + c = a + (b + c): Using the additive inverse property, a + (− a) = 0: Using the additive identity

signs, add their absolute values and prefix the sum with the common sign. Example: B) To add two numbers with unlike signs, find the difference between their absolute values, and prefix the result with the sign of the number with the greater absolute value. Example: C) To subtract a number b from another number a, change the sign of b and add to a. Examples: D) To multiply (or divide) two numbers having like signs, multiply (or divide) their absolute values and prefix the result with a