(I need to factor (x^2-16x+51) The best I can do is (x-17)(x-3) and this does not work!?

Answer 1

you have to use the QE formula
x=[16+/-rt(256-204)]/2
=[-16+/-rt52)]/2
=[-16+/-2rt13)]/2
=[2{-8+/-rt13}]/2
=-8+/-rt13

Answer 2

When you can't directly factor, use the quadratic formula

x = (16+/-√(256-204))/2

x = (16+/-2√(13))/2 = 8+/-√(13)

So the factored form would be

(x-8-√(13))*(x-8+√(13))

Answer 3

people like to use the formula so much O_o
however I think in this case completing the square is much easier

x^2 - 16x + 51

= x^2 - 16x + 64 - 13

= (x-8)^2 - (sqrt13)^2

then we know A^2 - B^2 factors to (A-B)(A+B)

thus

= (x-8-sqrt13) (x-8+sqrt13)

Answer 4

The factors are:

(x - 8 + √13) (x - 8 - √13);

Answer 5

x^2 - 16x + 51

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-(-16) ± sqrt((-16)^2 - 4(1)(51)))/(2(1))
x = (16 ± sqrt(256 - 204))/2
x = (16 ± sqrt(52))/2
x = (16 ± sqrt(4 * 13))/2
x = (16 ± 2sqrt(13))/2
x = 8 ± sqrt(13)

this problem can't be perfectly factored, but if you were to, it would look like

(x - (8 + sqrt(13)))*(x - (8 - sqrt(13)))

Answer 6

i just used the quadratic solution for x, where x = (-b plus/minus sqrt(b^2 - 4ac))/2a

we equate the solution to zero and then we get the factors.. :)

we get the factors
[x - 8 + sqrt(13)]
[x - 8 - sqrt(13)]

try this.. it works!