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).