# 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

 Jan 20, 2011 3rd degree polynomial by: Staff The question: By Mary (Afghanistan)4x^3-12x^2+8xThe 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 = 0The 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 = 04*x*x*x - 3*4*x*x + 2*4*x = 0As 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) = 0The 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) = 0The last step is to find the possible roots to the equationSince 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) = 01st factor: (4*x)(4*x) = 0Divide each side of the equation by 4(4*x)/4 = 0/4x*(4/4) = 0/4x*(1) = 0/4x*1 = 0/4x = 0/4x = 0, this is the first root 2nd factor: (1 - x)(1 - x) = 01 - x = 0Add x to each side of the equation1 - x + x = 0 + x1 + 0 = 0 + x1 = 0 + x1 = xx = 1, this is the second root3rd factor: (2 - x)(2 - x) = 02 - x = 0Add x to each side of the equation2 - x + x = 0 + x2 + 0 = 0 + x2 = 0 + x2 = xx = 2, this is the third and final rootthe final answer: the three roots to the original equation are x = 0, x = 1, and x = 2Thanks for writing.Staff www.solving-math-problems.com

 Jan 21, 2011 what its asking by: Anonymous i wrote it and its asking to simplify