SOLUTION: I am homeschooled with the School of Tomorrow. I have no teacher, and am struggling with factoring trinomials, particularly coefficients greater than one and complex factoring. R

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am homeschooled with the School of Tomorrow. I have no teacher, and am struggling with factoring trinomials, particularly coefficients greater than one and complex factoring. R      Log On


   



Question 181059: I am homeschooled with the School of Tomorrow. I have no teacher, and am struggling with factoring trinomials, particularly coefficients greater than one and complex factoring. Right now I am trying to solve 6X%5E2%2B14X%2B4 Please help me!
Found 2 solutions by Mathtut, josmiceli:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
%286x%2B2%29%28x%2B2%29
:
x=-1/3 and x=-2

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
6x%5E2+%2B+14x+%2B+4
To locate the roots, set the equation equal to 0
6x%5E2+%2B+14x+%2B+4+=+0
Divide both sides by 2
3x%5E2+%2B+7x+%2B+2+=+0
I often try to factor by trying combinations that will
factor the outside terms and try to get the inside term,
for instance:
(3x + ?)(x + ?) I've got the 1st term factored, now for the 3rd
(3x + 2)(x + 1) Does this work?
%283x+%2B+2%29%28x+%2B+1%29+=+3x%5E2+%2B+5x+%2B+2 not quite
How about
(3x + 1)(x + 2) ?
%283x+%2B+1%29%28x+%2B+2%29+=+3x%5E2+%2B+7x+%2B+2 that's it
----------------------
Some are not this neat, and you have to use the quadratic equation
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Use this when the form of the equation is
ax%5E2+%2B+bx+%2B+c+=+0
a+=+3
b+=+7
c+=+2
Some are not this neat, and you have to use the quadratic equation
x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29+
x+=+%28-7+%2B-+sqrt%28+49+-+24+%29%29+%2F+6+
x+=+%28-7+%2B-+sqrt%2825%29+%29+%2F+6+
x+=+%28-7+%2B-+5+%29+%2F+6+
x+=+-%287%2F6%29+%2B+%285%2F6%29
x+=+-%281%2F3%29
%28x+%2B+%281%2F3%29%29+=+0
and
x+=+-%287%2F6%29+-+%285%2F6%29
x+=+-%2812%2F6%29
x+=+-2
%28x+%2B+2%29+=+0
---------------
%28x+%2B+%281%2F3%29%29%28x+%2B+2%29+=+0
x%5E2+%2B+%287%2F3%29x+%2B+%282%2F3%29+=+0
Multiply both sides by 3
3x%5E2+%2B+7x+%2B+2+=+0