MAT1033 Lecture Notes - Lecture 17: Division Algorithm
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4. 3 polynomial division - the remainder and factor. Provide a generalization to each of the key terms listed in this section. = q (x) + r (x) g (x) (g (x))(cid:18) f (x) g (x)(cid:19) = (g (x))(cid:18)q (x) + r (x) g (x)(cid:19) f (x) = q (x) g (x) + r (x) If f (x) is being divided by x c, which would look like f (x) x c , then f (c) would be the remainder. Find the remainder when x2 3x + 5 is being divided by x 3. x 3 x = 3 x 3 = 0. = (3)2 3(3) + 5 x2 3x + 5. Find the remainder when 9x4 7x3 + 5x2 3x + 1 is being divided by x + 2. x + 2 x + 2 = 0 x = 2. = 9( 2)4 7( 2)3 + 5( 2)2 3( 2) + 1.
