Download ALGEBRA 2 6.0 CHAPTER 5

ALGEBRA 2 6.0
CHAPTER 5
You must be able to do the following for this assessment:
 Simplify monomial expressions involving positive, negative and variable exponents.
(Simplified form means: no powers of powers; each base appears only once; all fractions
are in simplest form; no negative exponents)
 Simplify any polynomial by combining like terms
 Given a polynomial determine its degree and leading coefficient (remember terms are not
always given in order from greatest to least).
 Add, subtract, multiply, and divide monomials and polynomials.
 Given a polynomial evaluate it for variables and algebraic expressions (i.e. find f(a)
orf(2k + 1) , see page 323 in the textbook.)
 Use synthetic division to divide a polynomial by a linear factor. Remember the divisor
must be in the form x – c, where c is a constant, and missing powers of the dividend
must be represented by zeros.
 Use long division to divide any two polynomials. Remember that missing powers of the
dividend must be represented by zeros and terms in the quotient must be placed above
the matching power in the dividend.
 Given a polynomial function (equation or graph) describe its end behavior in terms of
infinity (see page 324 in the textbook)
 Given the graph of a polynomial function:
o Determine whether it represents an even or odd function (based on its end
behavior)
o Determine the number of real zeros (or real roots). Remember that real zeros (or
real roots) are the x-intercepts.
o Estimate the x –coordinate at which any relative maximum or relative minimum
points (also called turning points) occur.
o Determine the smallest possible degree of the function. Remember that a
polynomial function of degree n has at most n – 1 turning points.
 Given an x-y chart for a polynomial function determine the consecutive integer values of
x between which real zeros are located. (y value must change from positive to negative
or from negative to positive.)
 Given an x-y chart for a polynomial function determine the consecutive integer values of
x between which relative maximum or relative minimum points are located. (y values
must be increasing and then decreasing or decreasing and then increasing)
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Factor polynomial expressions by using methods such as:
o Greatest common factor
o Difference of squares
o Sum or difference of cubes
o Quadratic form (by rewriting expressions of even degree greater that two in the
form of a quadratic expression)
o Grouping (group terms with a common factor, then factor out the common factor)
***Remember you cannot solve for x if you do not have an equation.***
Solve polynomial equations by factoring and using the Zero Product Property.
Use synthetic substitution to evaluate P(x) at a given value of x.
Use the Factor Theorem to determine if a given binomial is a factor of a given polynomial.
(x – r) is a factor of the polynomial P(x) if and only if P(r) = 0.
Given a polynomial equation determine the number of roots in the set of complex
numbers, including repeated roots. (A polynomial equation of degree n has exactly n
roots.)
Given a polynomial use Descarte’s Rule of Signs to determine the possible number of
positive real zeros, negative real zeros, and imaginary zeros.
Given two or more roots, real or imaginary, determine a polynomial function of least
degree with integral coefficients that has those roots. Remember that imaginary roots
must come in pairs (Complex Conjugate Theorem) and the polynomial function should be an
equation (f(x) = . . .)
Given a polynomial function with integral coefficients use the Rational Zero Theorem to
list all the possible rational zeros of the function.
Given a polynomial function and one factor, find the remaining factors.
Given a polynomial function
o Use the techniques listed above to determine all of the zeros of the function.
o Write the function in fully factored form as the product of linear factors.
o Sketch a rough graph of the function based on the zeros and the end behavior.
Given a word problem that can be solved by a polynomial equation of higher degree, define
the variable, write the polynomial equation, and solve.