In Example 9, change the 2x 3 to 2x + 3 and then determine whether 2x
Question:
In Example 9, change the 2x − 3 to 2x + 3 and then determine whether 2x + 3 is a factor.
Data from Example 9:
By using synthetic division, determine whether 2x − 3 is a factor of 2x3 − 3x2 + 8x −12.
We first note that the coefficient of x in the possible factor is not 1. Thus, we cannot use r = 3, because the factor is not of the form x − r. However 2x − 3 = 2(x − 3/2) which means that if 2(x − 3/2) is a factor. If we use r = 3/2 and find that the remainder is zero then x − 3/2 is a factor
Because the remainder is zero, x − 3/2 is a factor. Also, the quotient is 2x2 + 8, which may be factored into 2(x2 + 4). Thus, 2 is also a factor of the function. This means that 2(x − 3/2) is a factor of the function, and this in turn means that 2x − 3 is a factor. This tells us that 2x3 − 3x2 + 8x − 12 = (2x − 3) (x2 + 4)
Step by Step Answer:
Basic Technical Mathematics
ISBN: 9780137529896
12th Edition
Authors: Allyn J. Washington, Richard Evans