What is the H.C.F of $x^{2} + 2 x - 8, x^{3} - 4 x^{2} + 4 x, x^{2} - 4$
[4 Marks]

Open in App

Solution

Factors of :
$x^{2} + 2 x - 8 = (x + 4) (x - 2)$
[1 Mark]

$x^{3} - 4 x^{2} + 4 x = x (x - 2)^{2}$
[1 Mark]

$x^{2} - 4 = (x + 2) (x - 2)$
[1 Mark]

The highest common factor for the above expressions is $(x - 2)$
$∴$ H.C.F = $(x - 2)$
[1 Mark]

Suggest Corrections

Similar questions

x^{2} + 2 x - 8, x^{3} - 4 x^{2} + 4 x

x^{2} - 4

What is the H.C.F of $x^{2} + 2 x - 8, x^{3} - 4 x^{2} + 4 x, x^{2} - 4$

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

\frac{x^{2} - 7 x + 10}{x^{2} - 5 x - 14} \times \frac{x^{3} + 8}{x^{3} - 8} \times \frac{x^{2} + 2 x + 4}{x^{2} - 2 x + 4} \times \frac{x - 7}{x - 5} = ?

x^{2} - 4 x + 2 = 0

4 x^{2} + 2 x + \frac{4}{x} + \frac{16}{x^{2}}

Join BYJU'S Learning Program