SOLUTION: Factor the Polynomial 4x^3-28x^2+49x. First find the GCF of the terms 4x^3, 28x^2, and 49x, and factor it out of the polynomial 4x^3-28x^2+49x.Then use the appropriate pattern for

Question 203108: Factor the Polynomial 4x^3-28x^2+49x. First find the GCF of the terms 4x^3, 28x^2, and 49x, and factor it out of the polynomial 4x^3-28x^2+49x.Then use the appropriate pattern for factoring the remaining expression.
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Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Factor out the GCF:

The only factor common to all three terms is x. So the GCF is x. Factoring this out we get:

Next we will try to factor using patterns. The patterns which are most often taught are:

Difference of squares:
Difference of cubes:
Sum of cubes:
Perfect square trinomials:

Since the first three patterns factor binomials (two-term expressions) and since we have a trinomial (three-term expression), we will not be able to use the first three patterns. And since the fourth pattern has a "+" in front of the middle term and we have a "-", that pattern is out, too. The only possible pattern for is the last one: .

To see if our expression fits the pattern:

The first term in the pattern, means that the first term in our trinomial must be a perfect square. Since it is a perfect square. It is "2x squared". So our "a" is 2x.
The last term in the pattern is , a perfect square. So our last term has to be a perfect square (or we will not be able to use this pattern). Our last term, 49, is 7 squared. So it is a perfect square and our "b" is 7.
Last of all we need to see if our middle term fits the pattern's middle term which is 2ab. Since our "a" is 2x and our "b" is 7, 2ab = 2*(2x)*7 = 28x, our middle term!

Since all three terms of our trinomial fit the pattern of with "a" = 2x and "b" = 7, our trinomial will factor according to this pattern:

Now our complete expression is:

Remember, factoring is like reducing fractions: You keep going it until you can't go it any further. However, since will not factor any further, we are finished.
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