What will be the HCF of $(x^{2} + x), (x + 1)^{3}$ and $(x^{3} + 1)$ ?

(x^{3} + 1)

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

x (x + 1)^{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

(1 + x)^{3}

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

Open in App

Solution

The correct option is C $(x + 1)$
$x^{2} + x = x (x + 1)$
$(x + 1)^{3} = (x + 1) \times (x + 1) \times (x + 1)$
$x^{3} + 1 = (x)^{3} + (1)^{3} = (x + 1) (x^{2} - x + 1)$
Required $H . C . F . = (x + 1)$ .
Option C is correct.

Suggest Corrections

Similar questions

Q. Find the HCF of

f (x) = x^{3} + x^{2} - x - 1

and

g (x) = x^{3} + x^{2} + x + 1

$x + 1$ is a factor of the polynomial
$A .$ $x^{3} + x^{2} - x + 1$
$B .$ $x^{3} + x^{2} + x + 1$
$C .$ $x^{4} + x^{3} + x^{2} + 1$
$D .$ $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$

Question :

One of the factors of x⁵+x+1 is

(1) 2x² - x - 1

(2) x³ - x²+ 1

(3) x² - 2x² + 1

(4) x³ + x² + 1

Q. The HCF of

x^{2} - \frac{1}{x^{2}}, x^{2} - 2 + \frac{1}{x^{2}}

, and

x^{3} - \frac{1}{x^{3}} - 3 x - \frac{3}{x}

Q. Which of the following equations MUST be true, given that x is an integer ?
I.

x^{3} \geq {(- x)}^{3}

II.

\frac{x^{3}}{x} \geq \frac{x^{2}}{x}

III.

x (x + 1) \leq - x + x^{3}

Join BYJU'S Learning Program

What will be the HCF of (x2+x),(x+1)3 and (x3+1)?

The correct option is C (x+1)x2+x=x(x+1)(x+1)3=(x+1)×(x+1)×(x+1)x3+1=(x)3+(1)3=(x+1)(x2−x+1)Required H.C.F.=(x+1).Option C is correct.

What will be the HCF of $(x^{2} + x), (x + 1)^{3}$ and $(x^{3} + 1)$ ?

The correct option is C $(x + 1)$
$x^{2} + x = x (x + 1)$
$(x + 1)^{3} = (x + 1) \times (x + 1) \times (x + 1)$
$x^{3} + 1 = (x)^{3} + (1)^{3} = (x + 1) (x^{2} - x + 1)$
Required $H . C . F . = (x + 1)$ .
Option C is correct.