divide (x^3+2x^2+x+12)/x+3)?

Answer 1

It's kind of like doing long division, but with variables. Here's how you do it:

First, treat each term of the discriminant like a number. It makes it easier to conceptualize. The first term of the discriminant is x^3+2x^2, and our divisior is 'x+3'. In terms of variables, think of how many x's you can multiply to the divisor such that the discriminant is as small as possible.

Since we are dealing with a 'cubed' factor for the first part of the discriminant, we can multiply our divisor by x^2.

Thus, x^2 goes on top, and then multiply to solve for the remainder:

x^2(x+3) = x^3 + 3x^2. Subtracting this from x^3 + 2x^2, we have a remainder of -x^2. Now bring down the next factor of the discriminant, 'x', and perform the same algorithm:

(-x^2 + x)/(x + 3), we can divide multiply by an '-x' to get and '-x^2' term:

(-x)(x+3) = -x^2 - 3x. Subtracting from the discriminant -x^2+x, we get a remainder of '4x'. Now bring the final factor, '12'. Perform the division one last time:

(4x + 12)/(x+3). We can multiply by 4 to get a '4x' term.

4(x+3) = 4x+12. Subtracting from the discriminant, you have an OVERALL remainder of 0.

Thus, your solution is x^2-x+4

Basically, when you are trying to find what value to multiply to the divisor, you are trying to match the power of the discriminant value. Like in our first step, we tried to match 'x+3' with x^3. Thus you had to multiply 'x+3' by x^2 to get an x^3 term.

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Hope this helps and wasn't too confusing

Below is a website to help with these type of problems

Answer 2

x^2 -x_+4___________________________
x+3 |x^3 + 2x^2 +x + 12
x^3 + 3x^2
------------
-x2 +x
-x^2 -3x
------------------
4x +12
4x +12
---------
0

The answer is x^2 -x +4

I hope the above example shows the process.

There is a much easier way to divide a polynomial by a binomial called synthetic division. Look it up on the internet. It's quite easy to understand and you will like it because it saves much time.

Answer 3

Use synthetic division:
(x^3+2x²+x+12) / (x+3)
Follow the algorithm (from the source I provided) and you end up with a sequence of numbers:
1, -1, 4, 0

These correspond to the polynomial:
x² - x + 4

That is your answer.

Answer 4

x^2-x+4
x+3√x^3+2x^2+x+12
x^3+3x^2
-------------
-x^2+x
+x^2+3x
-----------
4x+12
-4x-12
--------
0

Check:
(x+3)(x^2-x+4)
x^3-x^2+4x+3x^2-3x+12
x^3+2x^2+x+12

I hope this helps!

Answer 5

Its like a long division problem.

. . . . . x^2 - x + 4
. . . . _ _ _ _ _ _ _ _ _ _ _
x + 3)x^3 + 2x^2 + x + 12
. . . . x^3 + 3x^2
. . . .- - - - - - - -
. . . . . . . - 1x^2 + x
. . . . . . . - 1x^2 - 3x
. . . . . . .- - - - - - - -
. . . . . . . . . . . .+ 4x + 12
. . . . . . . . . . . .+ 4x + 12
. . . . . . . . . . . .- - - - - - -

Answer 6

(x^3+2x^2+x+12) / (x+3)

........x^2 - x + 4
x + 3)x^3 + 2x^2 + x + 12
........x^3 + 3x^2
.................-x^2 + x + 12
.................-x^2 -3x
.........................4x + 12
.........................4x + 12
..................................0