Polynomial Long Division Review and Practice

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This content provides a detailed review on polynomial long division including step-by-step instructions, examples, and synthetic division practice problems. It covers topics such as descending polynomial order, solving binomial divisors, writing coefficients, determining remainders, and obtaining final answers. The included images further illustrate the processes involved in polynomial long division and synthetic division.

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Polynomial Long Division Review + + 3 2 1 A) y y y ( 6 )( ) 2 + + 3 2 x x x x 5 ( 13 10 ) 8 ( ) 2 B) 18 + y 0 2 + 3 6 y y x + 5 3 4 2 x 2 + + + + 3 2 y y y y 2 6 + + 3 2 x x x x 2 5 13 10 8

SYNTHETIC DIVISION: STEP #1:Be sure the polynomial is in stardanrd form with no gaps Descending Polynomial + + 3 2 x x x x 5 ( 13 10 ) 8 ( ) 2 + + 3 2 Order x x x : 5 13 10 8 STEP #2: Solve the Binomial Divisor = Zero (this is just the opposite of the constant in the divisor) ; 0 2 = = x = = x 2 STEP #3: Write the ZERO-value, then all the COEFFICIENTS of Polynomial. 2 5 -13 10 -8

5 -13 10 -8 10 2 -6 8 5 -3 0 = Remainder 4 STEP #4: Last Answer is your REMAINDER Write the coefficient answers in descending order starting with a Degree ONE LESS THAN Original Degree and include NONZERO REMAINDER OVER DIVISOR at end 5 x x + + 2 3 4 5 -3 4 + + = = 3 2 x x x x 5 ( 13 10 ) 8 ( ) 2 x + + 2 x 5 3 4 SAME ANSWER AS LONG DIVISION!!!!