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 = (25)/(3) \iff x=\pm\sqrt{(25)/(3)}=\pm(5)/(√(3))`

So, the polynomial can be written as

`3x^2-25 = \left(x-(5)/(√(3))\right)\left(x+(5)/(√(3))\right)`