Q. 1 C5.0( 1 Vote )

# Find the quotient and remainder using synthetic division.

(3x^{3} + 4x^{2} – 10x + 6) ÷ ( 3x – 2)

Answer :

Let p(x) = 3*x*^{3} + 4*x*^{2} – 10*x +* 6 be the dividend and arranging p(x) according to the descending powers of x.

Divisor, q(x) = 3x – 2

⇒ To find out Zero of the divisor –

q(x) = 0

3x – 2= 0

x =

So, zero of divisor is .

And, p(x) = 3*x*^{3} + 4*x*^{2} – 10*x +* 6

Put zero for the first entry in the second row.

∵ p(x) = (Quotient)×q(x) + remainder.

So, 3*x*^{3} + 4*x*^{2} – 10*x +* 6 = (x – )(3x^{2} + 6x – 6) + 2

= (3x – 2)(3x^{2} + 6x – 6) + 2

Thus, the Quotient = (3x^{2} + 6x – 6)= x^{2} + 2x – 2 and remainder is 2.

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

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