trinomials?

[after posting… this equation is NOT factorable…

the -5 is either a -2, or, if it is -5, then need to use the

quadratic equation as other have done above]

5x^2 – 5x – 3 = (ax+b)(cx+d)

where a, b, c and d tend to be integers.

If you foil this out….

ac(x^2) + (ad+bc)x +bd = 5x^2 – 5x – 3

a*c = 5

ad + bc = -5

b*d = -3

5 is a prime, so likely either a = +/-5, +/-1, or c = +/-5, +/-1

3 is a prime, so likely either b = +/-3, +/-1, or d = -+3, -/+1

ad + bc also must be negative.

You can guess and check.

Can substitute different sets of possible a,b,c, d and check the foil…

a*c = 5

b*d = -3

ad + bc = -5

a c b d

1 5 -3 1 …..

ac = 5 OK

bd = -3 OK

ad + bc = -13 NO

a c b d

1 5 3 -1 …..

ac = 5 OK

bd = -3 OK

ad + bc = 13 NO

a c b d

5 1 -3 1 …..

ac = 5 OK

bd = -3 OK

ad + bc = 2 NO

a c b d

5 1 3 -1 …..

ac = 5 OK

bd = -3 OK

ad + bc = -2 NO

?????

is the equation write (or is it too late for me).

a = 5, c=1, b=3, d=-1

(5x+3) (x-1) …. check,,, FOIL: 5x^2 -5x + 3x -3 = 5x^2 – 2x -3

x can be calculated as

x = (-b +/- sqrt(b^2 * 4 * a * c)) / (2 * a)

Here:

a = 5

b = -5

c = -3

x = (5 +/- sqrt((-5)^2 – 4 * 5 * -3)) / (2 * 5)

x = (5 +/- sqrt(25 + 60)) / 10

x = 5/10 +/- sqrt(85) / 10

x = .5 +/- sqrt(85) / 10

sqrt(85) = 9.22

x = .5 + .92 or .5 – .92

x = 1.42 or -.42

or 5 + or – the square root of 85 all over ten.

i think =]