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expressions - 3rd degree polynomial

by mary
(afghanistan)











































What can be done with the following 3rd degree polynomial?

4x^3-12x^2+8x

Can it be simplified?

Comments for expressions - 3rd degree polynomial

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Jan 20, 2011
3rd degree polynomial
by: Staff

The question:

By Mary
(Afghanistan)

4x^3-12x^2+8x

The answer:

The expression is already simplified.

Although you didn't say what you wanted, I assume you want to know how to calculate the roots of your expression if it is equal to zero.

4x^3 - 12x^2 + 8x = 0

The roots will be easy to calculate once the expression is factored. There will be three answers (roots).

Although it is not necessary, I?m going to expand the expression to make it easier to see how to begin to factor the expression.

4x^3 - 12x^2 + 8x = 0

4*x*x*x - 3*4*x*x + 2*4*x = 0

As you can see, each term contains a factor of 4*x.

We can factor out 4*x so that the equation now looks like this:

4*x*x*x - 3*4*x*x + 2*4*x = 0

(4*x)*(x*x - 3*x + 2) = 0

(4*x)*(x^2 - 3x + 2) = 0

The next step is to factor (x^2 - 3x + 2)

(4*x)*(x^2 - 3x + 2) = 0

(4*x)*(1 - x)*(2 - x) = 0

(4*x)(1 - x)(2 - x) = 0


The last step is to find the possible roots to the equation

Since the product of all three factors = 0, at least one of the factors must = 0. (0 * anything is still 0)

(4*x)(1 - x)(2 - x) = 0


1st factor: (4*x)

(4*x) = 0

Divide each side of the equation by 4

(4*x)/4 = 0/4

x*(4/4) = 0/4

x*(1) = 0/4

x*1 = 0/4

x = 0/4

x = 0, this is the first root


2nd factor: (1 - x)

(1 - x) = 0

1 - x = 0

Add x to each side of the equation

1 - x + x = 0 + x

1 + 0 = 0 + x

1 = 0 + x

1 = x

x = 1, this is the second root


3rd factor: (2 - x)

(2 - x) = 0

2 - x = 0

Add x to each side of the equation

2 - x + x = 0 + x

2 + 0 = 0 + x

2 = 0 + x

2 = x

x = 2, this is the third and final root

the final answer: the three roots to the original equation are x = 0, x = 1, and x = 2


Thanks for writing.


Staff
www.solving-math-problems.com


Jan 21, 2011
what its asking
by: Anonymous

i wrote it and its asking to simplify

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