Solve 3t^2-t

$$3 t ^ { 2 } - t$$

Factor

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

Solution Steps

Factor out t.

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

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.

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

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.

$$t=\frac{-\left(-1\right)±\sqrt{1}}{2\times 3}$$

Take the square root of 1.

$$t=\frac{-\left(-1\right)±1}{2\times 3}$$

The opposite of -1 is 1.

$$t=\frac{1±1}{2\times 3}$$

Multiply 2 times 3.

$$t=\frac{1±1}{6}$$

Now solve the equation t=\frac{1±1}{6} when ± is plus. Add 1 to 1.

$$t=\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$t=\frac{1}{3}$$

Now solve the equation t=\frac{1±1}{6} when ± is minus. Subtract 1 from 1.

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

Divide 0 by 6.

$$t=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{3} for x_{1} and 0 for x_{2}.

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

Subtract \frac{1}{3} from t by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$3t^{2}-t=3\times \frac{3t-1}{3}t$$

Cancel out 3, the greatest common factor in 3 and 3.

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

Evaluate

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