how do i divide:
x^3+2x^2+x+12 divided by x+3
can someone help>
Use polynomial long division, or synthetic division.
See
http://tutorial.math.lamar.edu/Classes/Alg/DividingPolynomials.aspx
for an example.
The answer is x^2 -x +4
Thank you, i have logged into the web you recommended.
no problem it is OK
how did you get this answer can you please write it out for me. I do not understand it.
Certainly! To divide the expression (x^3 + 2x^2 + x + 12) by (x + 3), you can use the long division method. Here's a step-by-step guide on how to do it:
Step 1: Start by writing down the dividend (the expression being divided) and the divisor (the expression you're dividing by) in the usual division format:
___________________
x + 3 | x^3 + 2x^2 + x + 12
Step 2: Look at the highest-degree terms of both the dividend and the divisor. In this case, it's x^3 divided by x, which gives us x^2. Write this as the first term of your quotient above the division bar:
x^2
___________________
x + 3 | x^3 + 2x^2 + x + 12
Step 3: Multiply x + 3 by x^2, giving you (x^2 * x) + (x^2 * 3) = x^3 + 3x^2. Write this result below the dividend, aligned with the corresponding terms:
x^2
___________________
x + 3 | x^3 + 2x^2 + x + 12
-(x^3 + 3x^2)
Step 4: Subtract the expression obtained in the previous step from your dividend. This will cancel out the x^3 terms:
x^2
___________________
x + 3 | x^3 + 2x^2 + x + 12
-(x^3 + 3x^2)
____________
-x^2
Step 5: Bring down the next term of the dividend (which is x). The new expression becomes -x^2 + x:
x^2 - 1
___________________
x + 3 | x^3 + 2x^2 + x + 12
-(x^3 + 3x^2)
____________
-x^2 + x
Step 6: Divide x + 3 into -x^2 + x. This gives us -1 as the next term of the quotient. Write it above the division line:
x^2 - 1
___________________
x + 3 | x^3 + 2x^2 + x + 12
-(x^3 + 3x^2)
____________
-x^2 + x
+(x^2 - 3x)
Step 7: Subtract the expression obtained in the previous step from your current dividend. This will cancel out the -x^2 terms:
x^2 - 1
___________________
x + 3 | x^3 + 2x^2 + x + 12
-(x^3 + 3x^2)
____________
-x^2 + x
+(x^2 - 3x)
_________________
4x
Step 8: Bring down the last term of the dividend (which is 12). The new expression becomes 4x + 12:
x^2 - 1 + 4
___________________
x + 3 | x^3 + 2x^2 + x + 12
-(x^3 + 3x^2)
____________
-x^2 + x
+(x^2 - 3x)
_________________
4x + 12
Step 9: Divide x + 3 into 4x + 12. This gives us 4 as the final term of the quotient. Write it above the division line:
x^2 - 1 + 4
___________________
x + 3 | x^3 + 2x^2 + x + 12
-(x^3 + 3x^2)
____________
-x^2 + x
+(x^2 - 3x)
_________________
4x + 12
-(4x + 12)
Step 10: Subtract the expression obtained in the previous step (4x + 12) from your current dividend (4x + 12). This will result in zero:
x^2 - 1 + 4
___________________
x + 3 | x^3 + 2x^2 + x + 12
-(x^3 + 3x^2)
____________
-x^2 + x
+(x^2 - 3x)
_________________
4x + 12
-(4x + 12)
_______________________
0
Step 11: Since the remainder is zero, we have successfully divided (x^3 + 2x^2 + x + 12) by (x + 3). The quotient is: x^2 - 1 + 4, which can be simplified to x^2 + 3.
Therefore, the division of (x^3 + 2x^2 + x + 12) by (x + 3) is equal to x^2 + 3.