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# Find the quotient and remainder using synthetic division.

(3x^{3} – 2x^{2} + 7x – 5) ÷ ( x + 3)

Answer :

Let p(x) = 3*x*^{3} – 2*x*^{2} + 7*x –* 5 be the dividend and arranging p(x) according to the descending powers of x.

Divisor, q(x) = x + 3

⇒ To find out Zero of the divisor –

q(x) = 0

x + 3 = 0

x = – 3

So, zero of divisor is – 3.

And, p(x) = 3*x*^{3} – 2*x*^{2} + 7*x –* 5

Put zero for the first entry in the second row.

∴ Quotient = 3x^{2} – 11x + 40

Hence, when p(x) is divided by (x – 1) the quotient is 3x^{2} – 11x + 40 and remainder is – 125.

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