(21x^3 - 7)/(3x - 1)(this one I cant get the anwswer to match up with my answer choices.)
Is there a way that I could use syntheic division?
what do you get?
7(3x^3-4)
Yes, you can use synthetic division to simplify the expression (21x^3 - 7) / (3x - 1) and potentially find the answer. Here is how you can do it:
Step 1: Write down the coefficients of the dividend (21x^3 - 7) in descending order of powers of x. In this case, the coefficients are 21, 0, 0, and -7.
Step 2: Set up the synthetic division by writing the divisor (3x - 1) to the left of the coefficients.
3x - 1 | 21 0 0 -7
Step 3: Bring down the first coefficient (21) and multiply it by the divisor (3x - 1). Write the result below the second coefficient.
3x - 1 | 21 0 0 -7
63x - 21
Step 4: Add the second coefficient to the result obtained in Step 3.
3x - 1 | 21 0 0 -7
63x - 21
__________________
21 63 0 -7
Step 5: Repeat Steps 3 and 4 until you have gone through all the coefficients.
3x - 1 | 21 0 0 -7
63x - 21
__________________
21 63 0 -7
63 0 0
______________
21 0 0 -7 0
Step 6: The remainders in the last row of the synthetic division are the coefficients of the simplified polynomial (21x^3 - 7) / (3x - 1).
In this case, the simplified polynomial is 21x^2 + 63 + (-7) / (3x - 1), which can be further simplified to (21x^2 + 56) / (3x - 1).
Make sure to double-check your work and see if this matches any of your answer choices.