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Remainder-Factor Theorem Example (2)
(x - 2)(x + 3)(x - 7) = x3 - 6x2 - 13x + 42 Let's check to see if 2, -3 and 7 go evenly into the polynomial. By substituting the roots into the equation we should get a value of 0 for y. (2)3 - 6(2)2 - 13(2) + 42 does evaluate to 0. (-3)3 - 6(-3)2 - 13(-3) + 42 does evaluate to 0. (7)3 - 6(7)2 - 13(7) + 42 does evaluate to 0. All 3 roots when inserted into the polynomial give us a 0 vlue for y, demonstrating our Factor and Remainder Theorem. |