3 6-1 Polynomial Functions A monomial is an expression that is either a real number, a variable or a product of real numbers and variables.A polynomial is a monomial or the sum of monomials.The exponent of the variable in a term determines the degree of that term.Standard form of a polynomial has the variable in descending order by degree.
11 6-2 Polynomials and Linear Factors If a linear factor of a polynomial is repeated, the zero is repeated. A repeated zero is called a multiple zero. A multiple zero has multiplicity equal to the number of times the zero occurs.
17 Polynomial Long Division Two people per worksheet.Take turns at each step, first partner decides what you multiply the divisor by, second partner agrees and does the multiplication, first partner agrees and does the subtraction, then switch for next term.You may do the work on the worksheet, paper or the white board. If you use the white board you must have me check EACH answer as you complete it.
18 Synthetic Divison Warm Up: Write a polynomial function in standard form with zeros at -1, 2 and 5.Use long division to divide:Use long division to dividex3 – 6x2 + 3x + 10x3 – x2 +1x3 – 2x2 –x + 6
34 6-5 Theorems about roots To find all the roots of a polynomial: determine the possible rational roots using the rational root theorem (ao/an)Use synthetic division to test the possible rational roots until one divides evenlyWrite the factored form and solve for all rootsUse the quadratic formula if necessaryYou may need to use synthetic division more than once
36 6-5 Theorems about roots Warm Up Find the polynomial equation in standard form that has roots at -5, -4 and 3Find f(-2) for f(x) = x4 – 2x3 +4x2 + x + 1 using synthetic divisionSolve x4 – 100 = 0
37 6-5 Theorems about roots Practice Problem: List all the possible rational roots of3x3 + x2 – 15x – 5 = 0Use synthetic division to determine which of these is a rootFactor and solve for the rest of the roots of the equation.
55 6-8 The Binomial Theorem Warm Up Find the zeros of the function by finding the possible rational roots and using synthetic division.multiply each and write in standard form:(x + y)2(x + y)3(x + y)4
56 6-8 The Binomial TheoremNotice that each set of coefficients matches a row of Pascal’s TriangleEach row of Pascal’s Triangle contains coefficients for the expansion of (a+b)nFor example, when n = 6 you can find the coefficients for the expansion of (a+b)6 in the 7th row of the triangle.Use Pascal’s Triangle to expand (a+b)6
57 6-8 The Binomial TheoremIf the terms of the polynomial have coefficients other than 1, you can still base the expansion on the triangle.
58 6-8 The Binomial TheoremEvaluate 4C0 4C1 4C2 4C3 4C4