simplify (6x^3-16x^2+11x-5)/(3x-2)
(3x-2)(2x-1)^2-3
my muliple choice is:
a)6x^2-12x+3 -9
3x-2
b)2x^2-4x+1 -9
3x-2
c)2x^2-4x+1 -1
3x-2
d)x^2+8x-3 -9
3x-2
the 3x-2's are all under the last number.
typo on b. the last number is 3 the signs are the same. im sorry for the confusion but the answer you gave me isnt an answer choice.
your cubic expression does not factor so you have to do a long division.
I got
(2x^2 - 4x + 1) - 3/(3x-2)
To simplify the expression (6x^3 - 16x^2 + 11x - 5) / (3x - 2), we can use long division. Here's a step-by-step guide:
Step 1: Divide the highest degree term in the numerator, 6x^3, by the highest degree term in the denominator, 3x. The result is 2x^2.
_________
3x - 2 | 6x^3 - 16x^2 + 11x - 5
2x^2
Step 2: Multiply the entire denominator, 3x - 2, by the result from Step 1, 2x^2. The product is 6x^3 - 4x^2.
_________
3x - 2 | 6x^3 - 16x^2 + 11x - 5
2x^2
-----------
6x^3 - 4x^2
Step 3: Subtract the result from Step 2 from the numerator.
_________
3x - 2 | 6x^3 - 16x^2 + 11x - 5
2x^2
-----------
6x^3 - 4x^2
- (6x^3 - 4x^2)
_________
-12x^2 + 11x - 5
Step 4: Bring down the next term, which is 11x, to the new numerator, -12x^2 + 11x - 5.
_________
3x - 2 | 6x^3 - 16x^2 + 11x - 5
2x^2
-----------
6x^3 - 4x^2
- (6x^3 - 4x^2)
------------------
-12x^2 + 11x - 5
Step 5: Divide the new highest degree term in the numerator, -12x^2, by the highest degree term in the denominator, 3x. The result is -4x.
_________
3x - 2 | 6x^3 - 16x^2 + 11x - 5
2x^2
-----------
6x^3 - 4x^2
- (6x^3 - 4x^2)
------------------
-12x^2 + 11x - 5
-12x^2 + 8x
Step 6: Multiply the entire denominator, 3x - 2, by the result from Step 5, -4x. The product is -12x^2 + 8x.
_________
3x - 2 | 6x^3 - 16x^2 + 11x - 5
2x^2
-----------
6x^3 - 4x^2
- (6x^3 - 4x^2)
------------------
-12x^2 + 11x - 5
-12x^2 + 8x
----------------
3x - 5
Step 7: Subtract the result from Step 6 from the numerator.
_________
3x - 2 | 6x^3 - 16x^2 + 11x - 5
2x^2
-----------
6x^3 - 4x^2
- (6x^3 - 4x^2)
------------------
-12x^2 + 11x - 5
-12x^2 + 8x
----------------
3x - 5
- (3x - 2)
_________
- 3
Step 8: Since we have no more terms to bring down and the remainder is -3, the simplified form of the expression is (2x^2 - 4x + 1) - (3 / (3x - 2)).
Therefore, the correct answer is:
b) 2x^2 - 4x + 1 - (3 / (3x - 2))