Question

Factor completely 3x^2+9x-33(x^2+3)3(x^2+3-1)3x(x^2+3x-1)prime​

Answer 1

Answer:

Answer from the answer data to choose from

3(x² + 3x - 1)

Factor completely

$3\left(x+\dfrac{3-\sqrt{13}}{2}\right)\left(x+\dfrac{3+\sqrt{13}}{2}\right)$

Step-by-step explanation:

$3x^2+9x-3=(3)(x^2)+(3)(3x)-(3)(1)\\\\=(3)(x^2+3x-1)\\\\\text{For}\ x^2+3x-1\ \text{use the quadratic formula}\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x^2+3x-1\to a=1,\ b=3,\ c=-1\\\\x=\dfrac{-3\pm\sqrt{3^2-4(1)(-1)}}{2(1)}=\dfrac{-3\pm\sqrt{9+4}}{2}=\dfrac{-3\pm\sqrt{13}}{2}=-\dfrac{3\pm\sqrt{13}}{2}\\\\3x^2+9x-3=3\left(x+\dfrac{3-\sqrt{13}}{2}\right)\left(x+\dfrac{3+\sqrt{13}}{2}\right)$