MATH 041 Lecture Notes - Lecture 9: Quadratic Formula, Coefficient
Document Summary
General polynomial f(x) = anxn + an-1xn-1 . All rational zeros must be of the form factor of a0 factor of an. Ex #1: f(x) = 2x4 7x3 10x2 + 33x + 18 left up, right up. Graph has at most 3 turning points. Rational zeroes form: (factors of 18) (factors of 2) = ( 1, 2, 3, 6, 9, 18) ( 1, 2) Suspects: -18, -9, -6, -9/2, -3, -2, -3/2, -1, -1/2, 18, 9, 6, 9/2, 3, 2, 3/2, To divide a polynomial by (x, -k), we list the coefficients of the polynomial in descending order of power remembering to substitute 0 in case of any missing powers. If the answer is 0 then that number is a rational zero of the equation. 2(x + 2) (x + ) (x 3)2 (2x + 4) (x + ) (x2 6x + 9) (2x2 + x + 4x + 2) (x2 6x + 9)
