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# Find the quotient and remainder using synthetic division.(3x3 + 4x2 – 10x + 6) ÷ ( 3x – 2)

Let p(x) = 3x3 + 4x2 10x + 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) = 3x3 + 4x2 10x + 6

Put zero for the first entry in the second row. p(x) = (Quotient)×q(x) + remainder.

So, 3x3 + 4x2 10x + 6 = (x – )(3x2 + 6x – 6) + 2

= (3x – 2) (3x2 + 6x – 6) + 2

Thus, the Quotient = (3x2 + 6x – 6)= x2 + 2x – 2 and remainder is 2.

Hence, when p(x) is divided by (3x – 2) the quotient is x2 + 2x – 2 and remainder is 2.

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