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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, nd the remaining factor and list zeros of f ....
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