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x 2 + 4x + 4

Trinomial Factoring




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Isabelle...I'm assuming you know what FOIL stands for...if not F - First O - Outer I - Inner L - Last Might I just add a small key to the previous answer which is correct. the two binomials will look something like: ( + ) ( + ) [right now, since the signs within the trinomial are positive, the signs inside the binomials will be positive. Your problem... x^2 + 4x + 4 the first term x^2(x squared) will be x times x, because that's how you get x^ ( x + ) ( x + ) The last term '4'...what are the numbers that when multiplied together will have a product of 4, there are: 1 x 4 and 2 x 2 correct, so its got to be either group of these numbers. These are the factors of 4. When you find the factors of the last value...instead of multiplying them, now add them together: 1 + 4 = and 2 + 2 = the answers being 5 and 4, right? Look at the middle value of your equation: x 2 + 4x + 4 which is 4x. The coefficient is 4(real number in front of the x). Which of the two groups of factors, when added together, equal 4? Its the 2 + 2 = right? Now put the two factors in the binomials: ( z + 2 ) ( x + 2 ). Complete the FOIL method and see if you get the trinomial: x 2 + 4x + 4 Now try it with some of your other problems...good luck.

A trinomial, if factorable, will factor into the product of two binomials. Since there is no common factor to extract and the coefficient of the first term is one, we can proceed with a simple process for factoring. 

In effect, we are undoing the process of "FOIL"ing. For example, 

(x + 2) (x - 1) = x2 - x + 2x - 2 = x2 + x - 2

So, you see the first term of the trinomial factors into the first binomial terms:

(x      ) (x       )

Now what about the last terms of the binomial? We look to the last term of the trinomial (-2). What two factors multiply to give -2, but sum to give the middle term? Well, the only two factors of for negative two are either (-1)(2) or (1)(-2). But which pair sums to give the middle term of +1? (-1)(2)

(x - 1) (x + 2)

For your problem, we do the same.

x2 + 4x + 4

Simply write out empty parentheses to start. Since the coefficient of the first term is 1, we can factor the first term into

(x        ) (x        )

Now, factors of 4 that could also sum the middle term, which is also 4. The sign on each factor must be positive to sum to the middle term.

1       4
+2       +2

(x   +  2) (x   +   2) ==> You can always FOIL this out to make sure the factorization is correct!