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Rufina [12.5K]
3 years ago
5

Factor completely 3X^2 -25​

Mathematics
1 answer:
Dominik [7]3 years ago
5 0

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)

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