Solve g(x)=3x^2-3x

$$g ( x ) = 3 x ^ { 2 } - 3 x$$

Factor

$$3x\left(x-1\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{2}-x\right)$$

Consider x^{2}-x. Factor out x.

$$x\left(x-1\right)$$

Rewrite the complete factored expression.

$$3x\left(x-1\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$3x^{2}-3x=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 3}$$

Take the square root of \left(-3\right)^{2}.

$$x=\frac{-\left(-3\right)±3}{2\times 3}$$

The opposite of -3 is 3.

$$x=\frac{3±3}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{3±3}{6}$$

Now solve the equation x=\frac{3±3}{6} when ± is plus. Add 3 to 3.

$$x=\frac{6}{6}$$

Divide 6 by 6.

$$x=1$$

Now solve the equation x=\frac{3±3}{6} when ± is minus. Subtract 3 from 3.

$$x=\frac{0}{6}$$

Divide 0 by 6.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 1 for x_{1} and 0 for x_{2}.

$$3x^{2}-3x=3\left(x-1\right)x$$

Evaluate

$$3x\left(x-1\right)$$