Expert: Scott A Wilson - 4/27/2010

Question
hi, my name is Nicholas and i was wondering if you could help me with a math problem?

i was wondering if you could help me with an algebra problem with factoring the trinomial?

my question is if you have 8x+24x+3 how would you factor this out?

Answer
The problem is written as 8x + 24x + 3, and that is (8+24)x + 3, which is 32x +3.

If trinomial means anything, though...
It says trinomial in the problem, so perhaps it is suppose to be f(x) = 8x³ + 24x + 3,
but using algebra, that can't be worked out.  Now f(-1) is negative and f(0) is positive.

The slope of that line can be seen to be f'(x) = 24x² + 24 = 24(x²+1)
{ f'(x) is called the derivative of f, which is the slope of f;
Note that the derivative of Ax is just A and the derivative of Bx² is 2Bx }.
The function f'(x) be seen to be always positive, so that means the function
always slopes upward, so there is only one root to f(x).  

What I think is the best method to use for finding the root is t is set equal to x - f(x)/f'(x).
This is repetetive and is known as Newton's method.  Start with x=0, and find t.
Once t has been found, set x to t and find a new value for t.

For the 1st time, x = 0, f(x) = 3, and f'(x) = 24, so t = 0 - 3/24 = -0.125.

For the 2nd time, taking the new x as t, we have
x is going to be -0.125, so f(-0.125) = -0.015625, f'(x) = 24.375,
so t = -0.125 - -0.015625/24.375 = -0.124358974.

For the 3rd time, again replacing x with t, we take
x as -0.124358974, so f(x) = -1.23063E-06, andf'(x) = 24.37116371,
so t = -0.124358974 - -1.23063E-06/24.37116371 = -0.124358924.

Note that this time, the value of t and the value of x are close to the same.
For the 4th time, we again take x as t and find a new t.
This time, however, t is the same as x since f(x) = 0 when we use t as x.

Study this and get it down, and then present this approach to your teacher.
Say you got it from a reliable source, and then point out it was from allexperts.com,
from who's known as mathguy.

To factor a binomial eqation, it is y = (-b±√(b²-4ac))/(2a).

Now if you're looking for some way to factor any trinomial, it is beyond what I can grasp.
In school, I learned a binomial equation was of the form ax²+bx+c and a trianomial equation
was of the form ax³+bx²+cx+d.