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Accelerated Algebra 2
Name:_________________________
Chapter 4 Study Guide
Date:__________________Pd:______
4-1: Polynomials
1. The degree of a monomial is ______________________________________________________________
2. The degree of a polynomial is _____________________________________________________________
3. Be able to distribute, add, and subtract in polynomials, then combine like terms and state the degree.
4-2 and 5-2: Exponents
1. When multiplying bases, _______________ exponents. Ex.
x 3 x 6 =_____________
2. When raising a power to a power, _______________ exponents. Ex.
3. When dividing bases, ________________ exponents. Ex.
4. A negative exponent means____________________. Ex.
5. A zero exponent means__________________. Ex.
(x 4 ) 3 =______
x5
=________________
x2
x 4 =________________
( x 2 y 3 ) 0 =_________________
6. Be able to simplify to all positive exponents. Review our exponent packet of notes, both quizzes, and book
problems.
4-3: Multiplying Polynomials
1. FOIL:_______________________________________________________________
2. (a+b)2=___________________________
3. (a-b)2=___________________________
4. (a+b)(a-b)=________________________
5. Also, be able to multiply 3 binomials, (x+1)(x-4)(x+6), or a binomial and trinomial, (x+6)(x2+3x+1).
4-4: Using Prime Factorization
1. Be able to find the prime factorization of a number.
2. To find GCF, take ____________ factors of the ____________ exponent.
3. To find LCM, take ____________ factors of the ____________ exponent.
4. Be able to do both for numbers, monomials, and polynomials (section 4-6).
4-5 and 4-6: Factoring
1. Perfect Square Trinomial (addition):_______________________________________
2. Perfect Square Trinomial (subtraction):____________________________________
a. Look for 3 terms
b. Look for perfect square first and last terms, even middle term
3. Difference of Squares:_________________________________________________
a. Look for 2 terms
b. Look for perfect squares
4. Sum of Cubes:_______________________________________________________
5. Difference of Cubes:___________________________________________________
a. Look for 2 terms
b. Look for perfect cubes
6. Factor by Grouping:
a. Try grouping 2 and 2, then factor each group to try to get a common factor, for example,
3x(y+2)-2(y+2)=(3x-2)(y+2).
b. Try grouping 3 and 1 to possibly get a difference of squares.
7. Factor all quadratics with x2 term, x4 term, or a coefficient that is not 1.
4-7: Solving Polynomial Equations
1. Steps to finding roots of polynomial equation:
a._________________________________________________________________________________
b._________________________________________________________________________________
c._________________________________________________________________________________
2. Solving for the zeros of a function: Set f(x)=0 and follow above steps.
3. What are double roots and double zeros? ___________________________________________________
_________________________________________________________________________________________
4. Be able to find the zeros on your calculator: Graph, then _________________________________________
_________________________________________________________________________________________
4-8: Problem Solving Using Polynomial Equations
1. Pythagorean Theorem:_________________________________________________
2. Consecutive Numbers:_________________________________________________
3. Consecutive Even or Odd Numbers:______________________________________
4. Area of Triangle:____________________ Area of Rectangle:__________________
5. Draw a picture if it applies!
4-9: Solving Polynomial Inequalities
1. Manipulate so 0 is on one side and highest degree variable’s coefficient is positive.
2. Factor.
3. Make a sign graph. Plot the roots that would make the equation = 0 and test numbers between each by
plugging into your factored polynomial. Take the places where your signs match your inequality. (Positive if >0
and negative if <0.)