Question

Factorise the polynomial
x2+3√2x - 8

Answer 1

The factorisation of $x^2+3\sqrt{2}x-8$ is $(x+4\sqrt{2})(x-\sqrt{2})$.

Step-by-step explanation:

The given polynomial:

$x^2+3\sqrt{2}x-8$

To find, the factorisation of $x^2+3\sqrt{2}x-8=?$

∴ $x^2+3\sqrt{2}x-8$

Split the middle term,

$=x^2+4\sqrt{2}x-\sqrt{2}x-8$

$=x(x+4\sqrt{2})-\sqrt{2}(x+4\sqrt{2})$

[ ∵ $8=4.\sqrt{2}.\sqrt{2}$]

$=(x+4\sqrt{2})(x-\sqrt{2})$

The factorisation of $x^2+3\sqrt{2}x-8=(x+4\sqrt{2})(x-\sqrt{2})$

Hence, the factorisation of $x^2+3\sqrt{2}x-8$ is $(x+4\sqrt{2})(x-\sqrt{2})$.