The polynomial, $x^{4} + 12 x^{2} + 64$ on factorization gives

(x^{2} - 2 x + 8) (x^{2} + 2 x - 8)

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

(x^{2} - 2 x - 8) (x^{2} + 2 x + 8)

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

(x^{2} + 2 x - 8) (x^{2} - 2 x - 8)

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

(x^{2} - 2 x + 8) (x^{2} + 2 x + 8)

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

Open in App

Solution

The correct option is D $(x^{2} - 2 x + 8) (x^{2} + 2 x + 8)$
Given the polynomial,
$x^{4} + 12 x^{2} + 64 = x^{4} + 16 x^{2} - 4 x^{2} + 64 = x^{4} + 16 x^{2} + 64 - 4 x^{2} = {(x^{2})}^{2} + 2 \cdot x^{2} \cdot 8 + 8^{2} - 4 x^{2} = {(x^{2} + 8)}^{2} - {(2 x)}^{2} = (x^{2} + 8 + 2 x) (x^{2} + 8 - 2 x) [∵ a^{2} - b^{2} = (a + b) (a - b)] = (x^{2} - 2 x + 8) (x^{2} + 2 x + 8) .$

Suggest Corrections