Q. 1 E5.0( 3 Votes )

# Find the quotient and remainder using synthetic division.(8x4 – 2x2 + 6x + 5) ÷ (4x + 1)

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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