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# Find the quotient and remainder using synthetic division.

x^{3} + x^{2} – 3x + 5) ÷ ( x – 1)

Answer :

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

p(x) = x^{3} + x^{2} – 3x + 5

Divisor, q(x) = x – 1

⇒ To find out Zero of the divisor –

q(x) = 0

x – 1 = 0

x = 1

So, zero of divisor is 1.

⇒ p(x) = x^{3} + x^{2} – 3x + 5

Put zero for the first entry in the second row.

∴ Quotient = x^{2} + 2x – 1

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

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