Question 96023
factor 

Use the ac test to determine if the following trinomial can be factored.  If it can be factored, find the values of m and n.

	3x² + 11x – 4

<pre><font size = 4><b>
Different books and different teachers use slightly different
terminology, so I'm not sure what you mean by "m and n".  However
I'll take you through the "ac" method and tell you what part I 
think your teacher means by "m and n".  But you should ask to make
sure.

<font color = "red">3</font>x² + 11x - <font color = "red">4</font>

1. Multiply the <font color = "red">3</font> by the <font color = "red">4</font>, get 12.

2. Notice the sign of the last term is -, so we think "DIFFERENCE".
(If the sign of the last term had been +, we would think "SUM")

3. Think of two positive integers which have product 12 and
DIFFERENCE 11, the coefficient (in absolute value) of the middle term.

It doesn't take long to see that two such positive integers are 
12 and 1.  That's because 12 TIMES 1 is 12 and 12 MINUS 1 is 11.

4. Now use 12 and 1 to rewrite the 11 as (12 - 1)

3x² + (12 - 1)x - 4

5. Remove the parentheses by distributing

3x² + 12x - 1x - 4

<i>[I think your teacher calls m = 12 and n = -1, the coefficients
of x above, but be sure to ask him/her.]</i>

6. Factor by grouping. That is:

a. Factor the first two terms by taking
out 3x.

b. Factor the last two terms by taking out -1

3x(x + 4) - 1(x + 4)

c. Now notice that <font color = "red">(x + 4)</font> is contained in both expressions:

3x<font color = "red">(x + 4)</font> - 1<font color = "red">(x + 4)</font>

d. So factor out the whole <font color = "red">(x + 4)</font> leaving 3x when factoring
it out of the left expression, and leaving -1 when factoring
<font color = "red">(x + 4)</font> out on the right expression.

<font color = "red">(x + 4)</font>(3x - 1)

That's it!

Edwin</pre>