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Algebra 2 Regents Review
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Key Concepts:
Terms in this set (19)
Division Algorithm for Polynomials
Dividend/Divisor = Quotient + Remainder/Divisor
Steps for Long Division of Polynomials
1. Set up the problem, where x-a is the divisor
2. Divide the 1st term of the dividend by the 1st term of the divisor. Put the quotient above the 2nd term in the dividend.
3. Multiply the divisor by the quotient and write the product under the dividend, properly aligning the terms. Now subtract this product from the dividend, and a term should cancel.
4. Repeat the same process, taking into account the locations of the monomials
5. write your final answer
Synthetic Division of Polynomials
1. Analyze if the divisor is in the form of (x-a), where x has a leading coefficient of 1. If not, and it's in the form of (Bx-a)|B E Z, you must divide by B at the conclusion of the problem!
2. Set x-a=0, and put a in the "window"
3. Line up the coefficients of the dividend. WARNING-do not skip powers!
4. Bring down the first coefficient, and multiply this number by the value of a. Write this number under the second number in the dividend. Repeat the process.
5. Write your answer in standard form using the resulting coefficients, reducing each power by one degree.
The Real Number System
Irrational Numbers
The Remainder Theorem
When the polynomial f (x) is divided by a binomial in the form of (x - a), the remainder equals f (a).
The Factor Theorem
If f (a) = 0 for polynomial f (x), then a binomial in the form of (x - a) must be a factor of the polynomial.
The order of factoring
Greatest Common Factor (GCF) -> Difference of Two Perfect Squares (DOTS) -> Trinomial (TRI) ->"AC" Method/Earmuff Method (AC)
GCF
ab + ab = a (b + c)
DOTS
x^2 - y^2 = (x + y)(x - y)
TRI
x^2 - x + 6 -> (x + 2)(x - 3)
Earmuff Method (AC)
Factor by Grouping
1. Group the first two terms and the last two terms. Re-arrange the original polynomial if necessary.
2. Factor out GCF in both; the resulting binomial must be the same.
3. Simply write in correct form
Factoring Perfect Cubes
SOAP
S - "Same" as the sign in the middle of the original expression
O - "Opposite" sign
AP - "Always Positive"
1. Take the cube root of each term
2. Write this result as a binomial, then
find the trinomial using the first
and last terms as a reference.
To add or subtract rational expressions, you need to find a
common denominator
Three steps to multiply rational expressions
factor first, reduce, and then multiply through
Steps to divide rational expressions
flip the second fraction, factor, reduce and then multiply through
Steps for complex fractions
Multiply each fraction by the LCD, cancel what's common and simplify
Solving rational equations
Find a common denominator, multiply each fraction only by what is "needed", solve for the equation in the numerator. Check answers when complete!
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