The factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2
The polynomial is given as:
2x^3 - 3x^2 - 5x + 6
Next, we test the factors
Option A. x + 6
Set the factor to 0
x + 6 = 0
Solve for x
x = -6
So, we set up the division as follows:
-6 l 2 - 3 -5 6
Bring down the leading coefficient
-6 l 2 - 3 -5 6
2
Multiply 2 and -6
-6 l 2 - 3 -5 6
-12
2
Add -3 and -12
-6 l 2 - 3 -5 6
-12
2 -15
Repeat this process
-6 l 2 - 3 -5 6
-12 72 -402
2 -15 67 -396
-396 is the remainder of the above division.
This means that x + 6 is not a factor of the polynomial
Option B. x - 2
Set the factor to 0
x - 2 = 0
Solve for x
x = 2
So, we set up the division as follows:
2 l 2 - 3 -5 6
Bring down the leading coefficient
2 l 2 - 3 -5 6
2
Multiply 2 and 2
2 l 2 - 3 -5 6
4
2
Add -3 and -12
2 l 2 - 3 -5 6
4
2 1
Repeat this process
2 l 2 - 3 -5 6
4 2 -6
2 1 -3 0
0 is the remainder of the above division.
This means that x - 2 is a factor of the polynomial
There is no need to check for the remaining options
Hence, the factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2
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