If $(x - 1)^{3}$ is a factor of $x^{4} + a x^{3} + b x^{2} + c x - 1$ , then the other factor is

x - 3

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

x + 1

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

x + 2

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

none of these

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

Open in App

Solution

The correct option is A $x + 1$
As, ${(x - 1)}^{3}$ is a factor of the polynomial,
So, $1$ is a repeated root be $(3$ times $)$ of the given equation.
Let the fourth root be $x,$ so $1, 1, 1, x = - 1$
$\Rightarrow x = - 1 \Rightarrow - 1$ is another root
Hence $(x + 1)$ is a factor

Suggest Corrections

Similar questions

x^{2} + x + 1

a x^{3} + b x^{2} + c x + d

a x^{3} + b x^{2} + c x + d = 0

If $(x - 1)$ is a factor of $a x^{3} - b x^{2} + c x$ , what is the value of $a^{3} - b^{3} + c^{3}$ ?

If (x-1) is a factor of $x^{4} + x^{3} - 2 x^{2} + x + 1$ . Find the other factor using the factor theorem.

(x + 3)

(x^{2} + 5 x + 7)

P (x) = a x^{3} + b x^{2} + c x + d

a

x^{4} + a x^{3} + b x^{2} + c x - 1 = 0

Join BYJU'S Learning Program