Solve 8p^2+7p

$$8 p ^ { 2 } + 7 p$$

Factor

$$p\left(8p+7\right)$$

Solution Steps

Factor out p.

$$p\left(8p+7\right)$$

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.

$$8p^{2}+7p=0$$

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.

$$p=\frac{-7±\sqrt{7^{2}}}{2\times 8}$$

Take the square root of 7^{2}.

$$p=\frac{-7±7}{2\times 8}$$

Multiply 2 times 8.

$$p=\frac{-7±7}{16}$$

Now solve the equation p=\frac{-7±7}{16} when ± is plus. Add -7 to 7.

$$p=\frac{0}{16}$$

Divide 0 by 16.

$$p=0$$

Now solve the equation p=\frac{-7±7}{16} when ± is minus. Subtract 7 from -7.

$$p=-\frac{14}{16}$$

Reduce the fraction \frac{-14}{16} to lowest terms by extracting and canceling out 2.

$$p=-\frac{7}{8}$$

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{7}{8} for x_{2}.

$$8p^{2}+7p=8p\left(p-\left(-\frac{7}{8}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$8p^{2}+7p=8p\left(p+\frac{7}{8}\right)$$

Add \frac{7}{8} to p by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$8p^{2}+7p=8p\times \frac{8p+7}{8}$$

Cancel out 8, the greatest common factor in 8 and 8.

$$8p^{2}+7p=p\left(8p+7\right)$$

Evaluate

$$p\left(8p+7\right)$$