You visited us 2 times! Enjoying our articles? Unlock Full Access!

Division of a Polynomial by a Polynomial

A polynomial ...

Question

A polynomial when divided by $(x - 6)$ gives a quotient $x^{2} + 2 x - 13$ and leaves a remainder $- 8$ . Then polynomial is

x^{3} + 4 x^{2} + 25 x - 78

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{3} - 4 x^{2} - 25 x + 70

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x^{3} - 4 x^{2} - 25 x - 70

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{3} + 4 x^{2} - 25 x + 78

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $x^{3} - 4 x^{2} - 25 x + 70$
Let $P$ be the polynomial. If $P$ is divided by $(x - 6)$ then it leaves a remainder $- 8$ and gives a quotient $x^{2} + 2 x - 13$ . Therefore, by applying division algorithm.

$P = (x - 6) (x^{2} + 2 x - 13) - 8 \Rightarrow P = x^{3} + 2 x^{2} - 13 x - 6 x^{2} - 12 x + 78 - 8 \Rightarrow P = x^{3} - 4 x^{2} - 25 x + 70$

Hence, the polynomial is $x^{3} - 4 x^{2} - 25 x + 70$ .

Suggest Corrections

Similar questions

p (x) = x^{3} - 4 x^{2} + 6 x - 2

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

r (x) = 8 x - 10,

a x^{3} + 4 x^{2} + 3 x - 4

x^{3} - 4 x + a

(x - 3)

a

p (x) = a x^{3} + 4 x^{2} + 3 x - 4

q (x) = x^{3} - 4 x + a

(x - 3)

a

p (x)

(x - 2) .

x^{3} + x^{2} + 1

x + 2

P (x) = x^{3} + 4 x^{2} - 5 x + 6

g (x) = x + 1

Join BYJU'S Learning Program