how to divide x^3 - x^2 - 22x + 13
by x^2 + 4x - 2.
Please Help!!! Please Hurry!!!!
*************_x___- 5___________________
x^2 + 4x - 2 |x^3 - 1 x^2 - 22 x + 13
**************x^3 + 4 x^2 - 2 x
**************----------------------
*******************-5 x^2 - 20 x + 13
*******************-5 x^2 - 20 x + 10
*******************-------------------
Remainder = 3
Thank you very much. This makes a lot more sense now. ;D
To divide the polynomial x^3 - x^2 - 22x + 13 by x^2 + 4x - 2, you can use long division. Here are the steps to follow:
Step 1: Write the dividend (x^3 - x^2 - 22x + 13) and the divisor (x^2 + 4x - 2) in standard form, arranged in descending order of degrees.
Step 2: Divide the first term of the dividend (x^3) by the first term of the divisor (x^2) to get x. Write this above the division line.
x
___________________
x^2 + 4x - 2 | x^3 - x^2 - 22x + 13
Step 3: Multiply the divisor (x^2 + 4x - 2) by the quotient (x). Write this new expression below the dividend, aligning like terms.
x
___________________
x^2 + 4x - 2 | x^3 - x^2 - 22x + 13
- (x^3 + 4x^2 - 2x)
Step 4: Subtract the expression obtained in Step 3 from the dividend. Write the result below the line.
x
____________________
x^2 + 4x - 2 | x^3 - x^2 - 22x + 13
- (x^3 + 4x^2 - 2x)
____________________
- 5x + 13
Step 5: Bring down the next term of the dividend (-5x) and repeat the process.
x - 5
____________________
x^2 + 4x - 2 | x^3 - x^2 - 22x + 13
- (x^3 + 4x^2 - 2x)
____________________
- 5x + 13
- (-5x + 20)
Step 6: Subtract the expression obtained in Step 5 from the result in Step 4.
x - 5
___________________
x^2 + 4x - 2 | x^3 - x^2 - 22x + 13
- (x^3 + 4x^2 - 2x)
____________________
- 5x + 13
- (-5x + 20)
____________________
-7
Step 7: The remainder obtained in Step 6 is -7.
Therefore, the quotient of x^3 - x^2 - 22x + 13 divided by x^2 + 4x - 2 is x - 5 with a remainder of -7.
So the final answer is (x - 5) with a remainder of -7.