Solve 2p-6p^2)

$$2 p - 6 p ^ { 2 } )$$

Factor

$$2p\left(1-3p\right)$$

Solution Steps

Factor out 2.

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

Consider p-3p^{2}. Factor out p.

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

Rewrite the complete factored expression.

$$2p\left(-3p+1\right)$$

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.

$$-6p^{2}+2p=0$$

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.

$$p=\frac{-2±\sqrt{2^{2}}}{2\left(-6\right)}$$

Take the square root of 2^{2}.

$$p=\frac{-2±2}{2\left(-6\right)}$$

Multiply 2 times -6.

$$p=\frac{-2±2}{-12}$$

Now solve the equation p=\frac{-2±2}{-12} when ± is plus. Add -2 to 2.

$$p=\frac{0}{-12}$$

Divide 0 by -12.

$$p=0$$

Now solve the equation p=\frac{-2±2}{-12} when ± is minus. Subtract 2 from -2.

$$p=-\frac{4}{-12}$$

Reduce the fraction \frac{-4}{-12} to lowest terms by extracting and canceling out 4.

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

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

$$-6p^{2}+2p=-6p\left(p-\frac{1}{3}\right)$$

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

$$-6p^{2}+2p=-6p\times \frac{-3p+1}{-3}$$

Cancel out 3, the greatest common factor in -6 and -3.

$$-6p^{2}+2p=2p\left(-3p+1\right)$$

Evaluate

$$2p\left(1-3p\right)$$