Factoring 3x^2 + 5x + 12

[TimberGhost0417]

I'm assuming ^ means " to the power of " so x^2 means x squared. I'm new here so that is the definition of ^ in this post. Please correct me if I'm wrong.

Here's my problem

3x^2+5x+12

Here's what I've done so far, and it usually works but I think I'm missing something.

3 multiplied by 12 = 36
I have to find something that, when multiplied, equals 36 and when added/subtracted to/from each other equals 5.

**Example Of How I Usually Factor Below***

3x^2+5x-12

3 multiplied by -12 = -36
-9 times 4 = -36
-9 + 4 = 5

So it comes out to:

3x^2 - 9x + 4x - 12
Factored out
3x(x-3) 4(x-3)

Use grouping

(x-3) (3x+4)

This is how I usually solve factoring questions but it doesn't work on this equation. 3x^2+5x+12

Please guide me and let me know how I'm supposed to solve this equation, from beginning to end. Thanks.

 

[arthur ohlsten]

3x^2+5x+12 factor

factors of 3 1,3
factors of 12 1,12 2,6 3,4
we want a set whose sum[+12 term] of products =5[x terms coefficients]
there are none proof use: quadratic equation
x=-5+/-[25-144]^1/2 all over 6
x=-5 +/- [-119]^1/2 all over 6
x=-5+/- i10.9 all over 6
x=-[5+i10.9]/6 x=-[5-i10.9]/6 these are the factors complex
Arthur

 

[TimberGhost0417]

Thanks for the reply, I'll be taking a look at the quadratic equations section in my textbook.

 

[Denis]

TG, you switched from 12 to -12 :shock:

 

[skeeter]

Re: Factoring

Hi there,

I'm assuming ^ means " to the power of " so x^2 means x squared. I'm new here so that is the definition of ^ in this post. Please correct me if I'm wrong.

ok here's my problem

3x^2+5x+12

Here's what I've done so far, and it usually works but I think I'm missing something.

3 multiplied by 12 = 36
I have to find something that, when multiplied, equals 36 and when added/subtracted to/from each other equals 5.

**Example Of How I Usually Factor Below***

3x^2+5x-12

3 multiplied by -12 = -36
-9 times 4 = -36
-9 + 4 = 5 no ... -9 + 4 - -5, not 5.

So it comes out to:

3x^2 - 9x + 4x - 12 3x^2 + 9x - 4x - 12
Factored out
3x(x-3) 4(x-3) 3x(x + 3) - 4(x + 3)

Use grouping

(x-3) (3x+4) (x + 3)(3x - 4)

This is how I usually solve factoring questions but it doesn't work on this equation. 3x^2+5x+12

Please guide me and let me know how I'm supposed to solve this equation, from beginning to end. Thanks.