I need help factoring a trinomial ?

Question

Does this factor? and if so what does it factor to?

9x^2 + 6x + 10

please help me this problem has been driving me crazy!

Answer 1

9x^2 + 6x + 10

= cannot be factored

Answer 2

Umm... I don't believe that's factorable lol

Unless you use the quadratic formula I guess... but you wouldn't get a pretty number.

Answer 3

To see if it is factorable use the discriminant, which is

                                   6^2-4*9*10=-324

since the discriminant is negative, the trinomial is not factorable over the reals, but it IS factorable over the complex numbers,

         (3x-(-1+3i))(3x+1+3i), where i^2=-1

Answer 4

This trinomial can't be factored. Even using the quadratic equation will give you "imaginary" numbers (a square root of a negative number is an imaginary number).

By using the "discriminant" you can determine the number of roots (real or imaginary) that your equation will have. The discriminant is part of the quadratic equation. The discriminant (D) = b^2 - 4ac

The discriminant (D) = b^2 - 4ac

1)If D > 0, the equation has 2 real solutions.

2)If D = 0, the equation has 1 real solution.

3)If D < 0, the equation has 2 conjugate imaginary solutions.

9x^2 + 6x + 10

a = 9, b = 6, c = 10

D = b^2 - 4ac

D = (6)^2 - 4(9)(10) = 36 - 360 = - 324

D is negative (condition #3) there are two imaginary solutions

Going all the way here ... using the quadratic equation:

- b +/- sqr root of b^2 - 4ac/2a

- 6 +/- sqr root 36 - 360/2(9)

- 6 +/- (sqr root - 324)/18    

- 6 +/-  18i/18

- 6/18 + 18i/18,  - 6/18 - 18i/18

- 1/3 + i , -1/3 - i     (ANSWERS)

That's why this problem was driving you crazy !!

Hope I helped.

Answer 5

this does not factor out. it is improbable.