Answer to Question #228631 in Algebra for Xavier

Question

40, The polynomial x⁶ – 8 is divisible by?

A.     X-√2

B.     X² + 2

C.     X³ -3

D.     None of the above

Answer 1

$(x^6-8)÷(x-\sqrt{2})$

$\frac{x^6-8}{x-\sqrt{2}}$

using $a^2-b^3=(a-b)(a+b),$ factor the expression

$\frac{(x^3-\sqrt8)×(x^3+\sqrt{8}}{x-\sqrt{2}}$

Simplify the expressions

$\frac{(x^3-2\sqrt2)×(x^3+2\sqrt{2}}{x-\sqrt{2}}$

Factor the expression

$\frac{(x-\sqrt2)×(x^2+\sqrt{2}+2)×(x^3+2\sqrt{2})}{x-\sqrt{2}}$

Reduce the fraction

$(x^2+\sqrt{2}x+2)×(x^3+2\sqrt{2})$

$x^5+2\sqrt{2}x^2+\sqrt{2}x^4+4x+2x^3+4\sqrt{2}$

Hence the polynomial $x-\sqrt2$