Answer to Question #97885 in Algebra for Alexandra

Question

Consider the expression
2 x 3 − 3 x 2 − 17 x − 12
. This expression has the following linear factors:
( x + 1 ) ( x − 4 ) ( 2 x + 3 )
. Which of those factors could not be the divisor when using synthetic division?

Answer 1

To use synthetic division, the divisor must be linear with a leading coefficient of 1.

Thus, the linear factor 2x+3 could not be the divisor when using synthetic division.

The factor x+3/2 could be the divisor.