The product of the HCF and the LCM of two polynomials is $(x^{2} - 1) (x^{4} - 1)$ then the product of the polynomials is _____

(x^{2} - 1) (x^{2} + 1)

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

(x^{2} - 1) {(x^{2} + 1)}^{2}

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

{(x^{2} - 1)}^{2} (x^{2} + 1)

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

None of these

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

Open in App

Solution

The correct option is D ${(x^{2} - 1)}^{2} (x^{2} + 1)$
We know that $H C F \times L C M =$ Product of the two polynomials.
So, Product of the two polynomials. $= (x^{2} - 1) (x^{4} - 1) = (x^{2} - 1) (x^{2} - 1) (x^{2} + 1) = {(x^{2} - 1)}^{2} (x^{2} + 1)$

Suggest Corrections

Similar questions

Which of the following polynomials below is identical to the polynomial $(x^{2} - 1) (x^{2} - 4)$ ?

p (x) = x^{3} - 1

q (x) = x^{3} + 1

r (x) = {(x^{2} + 1)}^{2} - x^{2}

x > 1

\frac{x}{x + 1} + \frac{x^{2}}{(x + 1) (x^{2} + 1)} + \frac{x^{4}}{(x + 1) (x^{2} + 1) (x^{4} + 1)} + \dots \infty

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

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

x^{2} + p x + q

x^{2} + a x + b is x + l

Join BYJU'S Learning Program