Solve 9k^2-21k

$$9 k ^ { 2 } - 21 k$$

Factor

$$3k\left(3k-7\right)$$

Solution Steps

Factor out 3.

$$3\left(3k^{2}-7k\right)$$

Consider 3k^{2}-7k. Factor out k.

$$k\left(3k-7\right)$$

Rewrite the complete factored expression.

$$3k\left(3k-7\right)$$

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.

$$9k^{2}-21k=0$$

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.

$$k=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}}}{2\times 9}$$

Take the square root of \left(-21\right)^{2}.

$$k=\frac{-\left(-21\right)±21}{2\times 9}$$

The opposite of -21 is 21.

$$k=\frac{21±21}{2\times 9}$$

Multiply 2 times 9.

$$k=\frac{21±21}{18}$$

Now solve the equation k=\frac{21±21}{18} when ± is plus. Add 21 to 21.

$$k=\frac{42}{18}$$

Reduce the fraction \frac{42}{18} to lowest terms by extracting and canceling out 6.

$$k=\frac{7}{3}$$

Now solve the equation k=\frac{21±21}{18} when ± is minus. Subtract 21 from 21.

$$k=\frac{0}{18}$$

Divide 0 by 18.

$$k=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{7}{3} for x_{1} and 0 for x_{2}.

$$9k^{2}-21k=9\left(k-\frac{7}{3}\right)k$$

Subtract \frac{7}{3} from k by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$9k^{2}-21k=9\times \frac{3k-7}{3}k$$

Cancel out 3, the greatest common factor in 9 and 3.

$$9k^{2}-21k=3\left(3k-7\right)k$$

Evaluate

$$3k\left(3k-7\right)$$