When you are looking for a factor of a polynomial, how do you know what binomials to try?

 

In Try This 3 you will explore patterns that will help you determine which factors to try when you are trying to factor a polynomial.

 

Try This 3

1.  
   1. Use the factor theorem to determine if the following binomials are factors of the polynomial. Record your results in a table similar to the one that follows.
   2. Use the polynomials and factors listed in the table to determine the a-value of each factor. The first polynomial is already completed.
      
      

      Polynomial	Constant Term	Factors x – a	a
      P(x) = x3 + 2x2 − 5x − 6	−6	x − 2	2
      		x + 1	−1
      		x + 3	−3
      P(x) = x3 + x2 − 10x + 8	8	x − 1
      		x − 2
      		x + 4
      P(x) = x4 + 2x3 − 13x2 − 14x + 24	24	x − 1
      		x − 3
      		x + 2
      		x + 4

2. Compare the value of the constant term in each polynomial to the value of a, and describe any patterns you find.
3. Try the pattern you discovered in question 2 and state the possible values of a for the polynomial P(x) = x3 − 6x2 + 5x + 12.

Save your responses in your course folder.