Divide the polynomial p(x) by g(x) and find the quotient and the remainder in each of the following.
p(x) = $x^{3}$ − 3 $x^{2}$ + 5x – 3, g(x) = $x^{2}$ − 2

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Quotient = x − 3, Remainder = 7x − 9

Quotient = x − 3, Remainder = 5x − 4

Quotient = x − 1, Remainder = 7x − 9

Quotient = x − 1, Remainder = 5x − 4

answer is A.

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Detailed Solution

We are asked to divide the polynomial p(x) =

x^{3}

− 3

x^{2}

+ 5x – 3 with the polynomial g(x) =

x^{2}

− 2
We need to find the quotient and remainder for this division.
So, now let us divide the given polynomials.
x - 3

x^{2}

– 2)

\underset{̲}{x^{3} - 3 x^{2} + 5 x - 3}

x^{3} - 2 x

\underset{̲}{- 3 x^{2} + 7 x - 3}

- 3 x^{2} + 6

\underset{̲}{7 x - 9}

Now we need to divide 7x−9 with x2 − 2. But the first term in 7x−9, that is 7x. We can see that degree of the obtained polynomial, that is 7x − 2, is less than the degree of the divisor. So, we cannot divide it.
So, it is the remainder of the above division.
So, from the above we get the quotient as x−3 and the remainder as 7x−9.
Hence the answer is Quotient = x − 3, Remainder = 7x − 9.
So, option (1) is correct.

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