Question

Factor completely 3X^2 -25​

Answer 1

In order to factor a polynomial, you have to find its roots

$x_1,\ x_2,\ldots,x_n$

So that you can factor it as

$p(x)=(x-x_1)(x-x_2)\cdots(x-x_n)$

So, in this case, we're looking for the solutions of

$3x^2-25=0 \iff 3x^2=25 \iff x^2 = \dfrac{25}{3} \iff x=\pm\sqrt{\dfrac{25}{3}}=\pm\dfrac{5}{\sqrt{3}}$

So, the polynomial can be written as

$3x^2-25 = \left(x-\dfrac{5}{\sqrt{3}}\right)\left(x+\dfrac{5}{\sqrt{3}}\right)$