Today in Pre-Calculus Need a calculator Review Chapter 2 Homework

Finding zeros Find all the exact zeros of f(x) = x4 – 2x3 – x2 – 4x – 6 and identify the zeros as real or nonreal and rational or irrational. Show all work. No decimal answers, any irrational zeros must be left in radical form.

Polynomial Long Division Use polynomial long division to rewrite Put answer in fractional form.

Degree of Polynomial If the polynomial is in standard form, find the highest power, this is the degree of the polynomial. example: f(x) = 5x3 – 4x5 +7x2 – 8x +12 If the polynomial is in factored form, add up the exponents for each of the factors. example: f(x) = (x – 7)(x + 2)3(x + 5)2

Multiplicity of a Zero If f is a polynomial function and (x – c)m is a factor of f, then c is a zero of multiplicity m. (c is a repeated zero). Example: f(x) = (x – 2)3(x+1)2 If the multiplicity is odd, then the graph crosses the x-axis at (c,0) and the value of f changes sign at x = c If the multiplicity is even, then the graph touches (but does not cross) the x-axis at (c,0) and the value of f does NOT change sign at x = c

Sketch the graph f(x) = (x – 2)3(x+1)2

Solving Inequalities Without graphing find the intervals where f(x) = 0 or UND f(x)>0 f(x)<0