Q. 1 E5.0( 3 Votes )

Find the quotient and remainder using synthetic division.

(8x4 2x2 + 6x + 5) ÷ (4x + 1)

Answer :

Let p(x) = 8x4 2x2 + 6x – 5 be the dividend. Arranging p(x) according to the descending powers of x and insert zero for missing term.


p(x) = 8x4 + 0x3 2x2 + 6x – 5


Divisor, q(x) = 4x + 1


To find out Zero of the divisor –


q(x) = 0


4x + 1 = 0


x =


zero of divisor is .


And, p(x) = 8x4 + 0x3 2x2 + 6x – 5


Put zero for the first entry in the 2nd row.



p(x) = (Quotient)×q(x) + remainder.


So, 8x4 2x2 + 6x – 5 = (x + )( 8x3 – 2x2 x + ) + ()


= (4x + 1)(8x3 – 2x2 x + )


Thus, the Quotient = (8x3 – 2x2 x + )= (2x3 x2 x + ) and remainder is .


Hence, when p(x) is divided by (4x + 1) the quotient is (2x3 x2 x + ) and remainder is .


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