Report

April 7, 2015 Polynomial Long Division Divide by w – 3. 3 2 3 x 2 x 4 x 3 by x 2 3x 3 . Divide Synthetic Division Divide x 2 5 x 6 by x – 1. 3 Divide 3x 6 x 2 by x – 2. Remainder Theorem If dividing f(x) by x – a, f(a) will determine the remainder. 3 What is the remainder when dividing x 7 x 6 by x – 4? Use the Remainder Theorem to evaluate f (x) = 6x3 – 5x2 + 4x – 17 at x = 3. Factor Theorem When dividing polynomials, if the remainder is zero, then the divisor is a factor. Use the Factor Theorem to determine whether x – 1 is a factor of f (x) = 2x4 + 3x2 – 5x + 7. Using the Factor Theorem, verify that x + 4 is a factor of f (x) = 5x4 + 16x3 – 15x2 + 8x + 16. Finding Exact Irrational Zeros Find the exact zeros for the function. Identify each zero as rational or irrational. Writing Functions w/ Given Conditions If the zeros of the function are -3, 7, and -1, and the leading coefficient is 4, write an equation for the function. Rational Zeros Theorem Given a function with constant of p and leading coefficient of q, all possible rational zeros can be found by factors of p factors of q 3 2 Find the possible rational zeros of f ( x) 2x 7 x 8x 6. Find the possible rational zeros of g ( x) 3x3 5x2 9x 16 Upper and Lower Bounds Test When dividing polynomials, if the quotient polynomial has all non-negative coefficients, then the “k” value is an upper bound. If the quotient polynomial has alternating sign coefficients, then the “k” value is a lower bound. Show that all real roots of the equation f ( x) x5 5x3 10x2 12x 20 lie between - 4 and 4.