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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.)