Q. 1 E5.0( 3 Votes )

# Find the quotient and remainder using synthetic division.

(8x^{4} – 2x^{2} + 6x + 5) ÷ (4x + 1)

Answer :

Let p(x) = 8*x*^{4} – 2*x*^{2} + 6*x –* 5 be the dividend. Arranging p(x) according to the descending powers of x and insert zero for missing term.

p(x) = 8*x*^{4} + 0x^{3} – 2*x*^{2} + 6*x –* 5

Divisor, q(x) = 4*x* + 1

⇒ To find out Zero of the divisor –

q(x) = 0

4x + 1 = 0

x =

zero of divisor is .

And, p(x) = 8*x*^{4} + 0x^{3} – 2*x*^{2} + 6*x –* 5

Put zero for the first entry in the 2^{nd} row.

∵ p(x) = (Quotient)×q(x) + remainder.

So, 8*x*^{4} – 2*x*^{2} + 6*x –* 5 = (x + )( 8x^{3} – 2x^{2} – x + ) + ()

= (4x + 1)(8x^{3} – 2x^{2} – x + )

Thus, the Quotient = (8x^{3} – 2x^{2} – x + )= (2x^{3} – x^{2} – x + ) and remainder is .

Hence, when p(x) is divided by (4x + 1) the quotient is (2x^{3} – x^{2} – x + ) and remainder is .

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