You visited us 1 times! Enjoying our articles? Unlock Full Access!

Division Algorithm for a Polynomial

On dividing a...

Question

On dividing a polynomial $3 x^{3} + 4 x^{2} + 5 x - 13$ by a polynomial g(x), the quotient and the reminder were $3 x + 10$ and $16 x - 43$ respectively. Find the polynominalg(x).

Open in App

Solution

Let $g (x) = y$
Now we know that
$d i v i s o r \times q u o t i e n t + r e m a i n d e r = d i v i d e n d$
$y (3 x - 110) + 16 x - 43 = 3 x^{2} + 4 x^{2} + 5 x - 13$
$y (3 x - 110) = 3 x^{2} + 4 x^{2} - 11 x + 30$
$y = \frac{3 x^{2} + 4 x^{2} - 11 x + 30}{3 x + 10}$
$y = x^{2} - 2 x + 3$

Suggest Corrections

Similar questions

3 x^{3} + 4 x^{2} + 5 x - 13

g (x)

(3 x + 10)

(16 x - 43)

g (x)

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

g (x)

(3 x - 5)

(9 x + 10)

g (x)

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

g (x)

x - 2

- 2 x + 4

g (x)

On dividing x^3-8x3^2+20x-10 by a polynomial g(n) the quotient and the reminder where x-4 and 6 respectively find g(n)

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

g (x) = x^{2} + 2 x + 1

r (x) = 9 x + 10

q (x)

Join BYJU'S Learning Program