P x d x Q x R x Dividend Divisor Quotient Remainder 2 3 Divide each using long

P x d x q x r x dividend divisor quotient remainder 2

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P ( x ) = d ( x ) • Q ( x ) + R ( x ) Dividend Divisor Quotient Remainder 2.
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3. Divide each using long division and determine if the denominator is a factor of the numerator: 322 14 3 2 2 5 4. 1 x x x x + a. b. 3 2 2 5 4. 3 x x x x + + c.
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4. The Remainder Theorem If a number c is substituted for x in a polynomial f ( x ), then the result f ( c ) is the remainder that would be obtained by dividing f ( x ) by x c . That is, if f ( x ) = ( x c ) • Q ( x ) + R , then f ( c ) = R . Synthetic division is a collapsed version of long division; only the coefficients of the terms are written.
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5. Divide using synthetic division: a. b. ( ) 5 4 3 2 4 6 2 50 ( 2) x x x x x + + + + ( ) 3 2 2 7 5 ( 3) + + x x x
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6. Use synthetic division to determine if 4 is a factor of f ( x ). f ( x ) = x 3 6 x 2 + 11 x 6
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