SOLUTION: How do i factor the following polynomial. x to the 3rd power + 2x to the 2nd power + 3x + 6 ?

Question 355830: How do i factor the following polynomial. x to the 3rd power + 2x to the 2nd power + 3x + 6 ?

Found 2 solutions by Alan3354, jsmallt9:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!

Notice that the coefficients 1, 2 & 3 add to 6, the last one.
Try x = 1 and -1 first.
Sub them, see if you get zero.
Since all the terms are positive, +1 won't work. In fact, no + real numbers will work.
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Try -1, then -2, etc.
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Once you find the first term, then it's 2nd order and simpler.

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Another tutor's response uses the factoring method which is trial and error of the possible rational roots. This method can work on this problem but as you can see, there can be a lot of "miss" in a "hit or miss" method.

The four terms in the expression are too many for any of the factoring patterns commonly taught. And there are also too many terms for trinomial factoring. But another factoring technique which can work on the expression is factoring by grouping. This is where you find subexpressions which have a Greatest Common Factor (GCF) and then, if you're lucky, the two factored subexpressions will have a common factor between them.

So we will factor out the GCF of the first two terms, which is , and the GCF of the last two terms, which is 3:

And as we can see, the two factored subexpressions have a common factor between them: (x+2). We can factor out this common factor from the two subexpressions:

Neither of these factors will factor further so this is the answer.

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