The HCF of $x^{5} + 2 x^{4} + x^{3} a n d x^{7} - x^{5}$ is

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

x (x + 1)

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

x^{3}

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

x^{3} (x + 1)

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

Open in App

Solution

The correct option is D $x^{3} (x + 1)$
$x^{5} + 2 x^{4} + x^{3} a n d x^{7} - x^{5}$
$\Rightarrow x^{3} (x^{2} + 2 x + 1) \Rightarrow x^{3} (x + 1) (x + 1)$
$x^{7} - x^{5} \Rightarrow= x^{5} (x^{2} - 1) \Rightarrow x^{5} (x + 1) (x - 1)$
$∴ R e q u i r e d H . C . F = x^{3} (x + 1)$

Suggest Corrections

Similar questions

The HCF for $x^{5}$ , $x^{3}$ , $x^{2} + x$ is___

Find the polynomial from the given information.

Quotient = x^{3} + 2 x

Divisor = x^{2} + \frac{1}{2} x

Remainder = 5

\frac{x}{1 - x^{2}} - \frac{x^{3}}{1 - x^{6}} + \frac{x^{5}}{1 - x^{10}} - . . . . . . . = \frac{x}{1 + x^{2}} + \frac{x^{3}}{1 + x^{6}} + \frac{x^{5}}{1 + x^{10}} + . . . . .

x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8

x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8

$x^{5} + x^{4} + x^{3} + x^{2} + x + 1$ by $x^{3} + 1$

Join BYJU'S Learning Program