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# section33 - r x is Example Divide f x = x 3-5 x 2-11 x 8 by...

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MAT 111 - College Algebra Section 3.3 Polynomial Division Objectives: 1. Learn how to divide a polynomial by another polynomial. 2. Learn the Remainder theorem. 3. Learn the Factor theorem. 1. There are two ways to divide a polynomial by another polynomial: (a) Using long division. (b) Using synthetic division (works when the divisor is in linear form). Examples: (a) Use long division to divide 4 x 3 - 7 x 2 - 11 x + 5 by 4 x + 5. (b) Find the quotient and remainder when x 5 + 7 is divided by x 3 - 1.

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On dividing a polynomial function f ( x ) by another polynomial function d ( x ) we get a quotient q ( x ) and a remainder r ( x ) with r ( x ) = 0 or degree of r is strictly less than degree of d . The polynomial function f ( x ) can then be written as f ( x ) = d ( x ) q ( x ) + r ( x ) Dividend = Divisor Quotient + Remainder If r ( x ) = 0, then d ( x ) divides the polynomial f ( x ) and we have found a factor of the polynomial. If the divisor, d ( x ) is a linear function, then the degree of the remainder
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Unformatted text preview: r ( x ) is . . . . Example: Divide f ( x ) = x 3-5 x 2-11 x + 8 by x + 2. 2. If the divisor d ( x ) is of the form x-c , then the remainder is . . . Example: Find the remainder on dividing f ( x ) = x 3-4 x 2 + 2 x-5 by x + 2. 3. (a) If f ( c ) = 0 , then x-c is a factor of f ( x ) . (b) If x-c is a factor of f ( x ) , then f ( c ) = 0 Examples: (a) Determine whether x-2 is a factor of f ( x ) = x 3-7 x + 6 or not. (b) Use long division to show that x = 2 3 is a zero of f ( x ) = 48 x 3-80 x 2 + 41 x-6 and use the result to factor the polynomial completely. List all real zeros of the function. (c) Given that x + 3 and x-2 are two factors of f ( x ) = 3 x 3 + 2 x 2-19 x + 6, ﬁnd the remaining factor and list zeros of f ....
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section33 - r x is Example Divide f x = x 3-5 x 2-11 x 8 by...

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