Find the quotient and remainder obtained when $p (x) = 3 x^{2} - 5 x + 2$ is divided by $g (x) = x + 2$ .

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Solution

Since $p (x)$ and $g (x)$ are any polynomial of degree greater than or equal to one.

$p (x) = 3 x^{2} - 5 x + 2 g (x) = x + 2$ .

$p (x)$ is the dividend and $g (x)$ in the divisor.

$x + 2) 3 x^{2} - 5 x + 2 (3 x - 11 3 x^{2} + 6 x - - — - - - - - - - - - 11 x + 2 - 11 x - 22 + + — - - - - - - - - 24$

Hence, $3 x - 11$ is the required quotient and $24$ is the remainder.

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Q. Find the quotient and the remainder when:

f (x) = x^{3} - 3 x^{2} + 5 x - 3

is divided by

g (x) = x^{2} - 2

Question 1 (i)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

$p (x) = x^{3} - 3 x^{2} + 5 x - 3, g (x) = x^{2} - 2$

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$(p x) = 2 x^{3} + 3 x^{2} - 11 x - 3, g (x) = (x + \frac{1}{2})$ .

Q. Find the quotient and remainder when p(x)=

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

is divided by g(x)=

x^{2} - 2

Q. Divide the polynomial

p (x)

by the polynomial

g (x)

and find the quotient and remainder.

p (x) = x^{3} - 3 x^{2} + 5 x - 3

g (x) = x^{2} - 2

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Find the quotient and remainder obtained when p(x)=3x2−5x+2 is divided by g(x)=x+2.

Find the quotient and remainder obtained when $p (x) = 3 x^{2} - 5 x + 2$ is divided by $g (x) = x + 2$ .