SOLUTION: Factor completely. x^2 + 3x � 28

Question 89097: Factor completely.
x^2 + 3x � 28

Found 2 solutions by josmiceli, bucky:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

The thing to notice is that certain factors of 28 are 4 and 7. Also,
the difference between them is . From this I get
. You just have to get the + and - signs right
If the problem was , then the answer would be

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
Since the multiplier of the term is 1, the factors of this polynomial must be
(presuming it factors) one of the following pairs of factors of 28:
.
(28 and 1)
(14 and 2)
(7 and 4)
.
Since 28 is preceded by a minus sign, in each factor pair, one of the numbers must be positive
and the other must be negative. If they both were positive or they both were negative,
they would multiply together to give +28.
.
Now look at the middle term in the polynomial ... the one that contains the "x". It is
multiplied by +3. Therefore, our factor pair must combine to give us +3.
.
There is no way that 28 and 1 can be added or subtracted to give +3. There is also no
way that 14 and 2 can be added or subtracted to give +3. But what about 7 and 4?
We already know that one of these two numbers must be positive and the other negative.
How about if the 7 were positive and the 4 were negative. If they were added the result
would be the +3 we are looking for. Therefore, we have figured out that +7 and -4 are what
we need. They multiply to give the -28 and they add to give the +3.
.
We can now form the factored answer of:
.
(x + 7)*(x - 4)
.
Check by multiplying:
.
x*x = x^2
x*(-4) = -4x
7*x = +7x
7*(-4) = -28
.
Combine these four products:
.

.
The two terms that contain "x" combine to be +3x so the answer becomes:
.

.
And since this is the polynomial that you were asked to factor, the two factors we found
are correct ... (x + 7)*(x - 4)
.
Hope this helps you to see how you can develop the answer.

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