factor this polynomial completely: r exponent 2-18r+21?

Answer 1

r^2 - 18r + 21

That doesn't factor. You would need to use the quadratic equation to solve it. (Are you sure you typed the equation correctly?)

Answer 2

r^2 - 18r + 21

r = (-b ± sqrt(b^2 - 4ac))/(2a)

r = (-(-18) ± sqrt((-18)^2 - 4(1)(21)))/(2(1))
r = (18 ± sqrt(324 - 84))/2
r = (18 ± sqrt(240))/2
r = (18 ± sqrt(16 * 15))/2
r = (18 ± 4sqrt(15))/2
r = 9 - 2sqrt(15) or 9 + 2sqrt(15)

Even though this can't be perfectly factored, here is how it would look in factored form

(r - (9 - 2sqrt(15)))(r - (9 + 2sqrt(15)))
or
(r - 9 + 2sqrt(15))(r - 9 - 2sqrt(15))