B. Factoring Trinomials Symbolically

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B. Factoring Trinomials Symbolically

Some trinomials can be factored using algebra tiles, but can these same trinomials be factored symbolically? Trinomials are often formed by multiplying two binomials. In the following investigation, you will look for patterns in binomial multiplications that result in a trinomial.

Investigation

The following table shows pairs of binomials and their products, in the form .

1. 
   

1. What do p and q represent in the binomial multiplication?
   
   

2. What do b and c represent in in the binomial multiplication?
   
   

2. 
   

1. In each row, compare the p and q values to the b-value. How are p, q, and b related?
   
   

2. In each row, compare the p and q values to the c-value in each row. How are p, q, and c related?
   
   

3. Write your own binomial multiplication of the form . Are the relationships you observed in part 2 true for your multiplication?
   
   

4. 
   

1. Predict p and q values for the factors of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«/math».
   
   

2. Write the factors of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«/math» using the p and q values from part a.
   
   

3. Verify the factors using multiplication.