How to answer this question? (6x2 - 5x + 4) / (2x + 1),,,,, 6x2 this 2 means x to the 2nd power.

Question

question reversion

(6x^2 - 5x + 4) / (2x + 4)

(6x^2 - 5x + 4) / (2x +1)

Answer 1

I don't think it factors evenly, but even if it does, you'll get the right solution with long division.

Take the term with highest degree of x (6x^2) in the numerator, and divide by the term with highest degree of x (2x) in the denominator. That's the first part of the solution.

6x^2 / 2x = 3x

Now, multiply that part of the solution by the denominator:

3x (2x + 1) =
6x^2 + 3x

... and subtract that from the numerator:

6x^2 - 5x + 4 - (6x^2 + 3x) =
6x^2 - 6x^2 - 5x - 3x + 4 =
-8x + 4

Take the term with highest degree of x (-8x) in what is left of the numerator, and divide by the term with highest degree of x (2x) in the denominator. That's the next part of the solution:

-8x/2x = -4

Now, multiply that part of the solution by the denominator:

-4 (2x + 1) =
-8x - 4

... and subtract that from what's left of the numerator:

-8x + 4 - (-8x - 4) =
-8x + 8x + 4 + 4 =
8

Since the degree of x in what is left of the numerator (x^0 since it is just "8") is smaller than the degree of x in the denominator, this is just the remainder. So the answer is the two parts of the solution we added up above:

3x - 4, with remainder 8.

Answer 2

You can set this kind of question up like a regular long division question, unless of course you can factor the numerator to give you the denominator as one of the factors - always try this first. In this case, 6x^2 - 5x +4 cannot be so factored. So, write it as a division question, (2x+1 into the numerator). 2x+1 will go into (6x^2-5x) 3x times - put that above the 5x. Multiply, and you get 6x^2+3x. Put that underneath and subtract, and you get -8x. Bring down the 4 to make -8x+4. Divide the 2x+1 into this, and you get -4 times. Multiply, you get +8. So the final answer is 3x-4 with +8 remainder. You can check by multiplying the (3x-4) by (2x+1), and then adding 8 to the answer.

Answer 3

If you divide 2x+1 into the numerator, you can get:
(6x^2-5x+4)/(2x+1) = (3x-4) + 8/(2x+1)

Answer 4

(6x^2 - 5x - 4) / (2x + 1)
= (3x - 4)(2x + 1) / (2x + 1)
= (3x - 4)

***** Note that I changed +4 to -4 above *****