Factor completely 5x^2-22x+21

To factor the quadratic expression 5x^2 - 22x + 21, we can use the factoring by grouping method or the quadratic formula.

Let's first try factoring by grouping:

5x^2 - 22x + 21

First, multiply the coefficient of the x^2 term (5) by the constant term (21).

5 * 21 = 105

Now, we need to find two numbers that multiply to give 105 and add up to the coefficient of the x term (-22).

The numbers -15 and -7 satisfy these conditions.

Split the -22x term using these numbers:

= 5x^2 - 15x - 7x + 21

Group the terms:

= (5x^2 - 15x) + (-7x + 21)

Take out the Greatest Common Factor (GCF) from each group:

= 5x(x - 3) - 7(x - 3)

Notice that (x - 3) is common to both groups.

Combine the terms:

= (5x - 7)(x - 3)

Therefore, the factored form of the quadratic expression 5x^2 - 22x + 21 is (5x - 7)(x - 3).