Divide the following polynomial p(x) by the polynomial S(x)
$P (x) = \frac{2}{3} x^{2} + 5 x + 6, S (x) = x + 6$ .

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Solution

We divide $\frac{2}{3} x^{2} + 5 x + 6$ by $(x + 6)$ as shown in the above image:

From the division, we observe that the quotient is $\frac{2}{3} x + 1$ and the remainder is $0$ .

Hence, the quotient is $\frac{2}{3} x + 1$ and the remainder is $0$ .

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Similar questions

p (x) = 2 x^{3} + 9 x^{2} + 13 x + 6, S (x) = 2 x^{2} + 5 x + 3

Statement1: The polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ when divided by $x - 1$ gives zero as the remainder.

Statement2: $(x - 1)$ is a factor of the polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ .

p (x)

g (x)

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

p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x

p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}

Divide the polynomial $p (x)$ by the polynomial $g (x)$ and find the quotient and remainder of the following.

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

The remainder of the polynomial P(x) = 3 $x^{2}$ + 5x + 8, when divided by x + 2 is___.

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