Need desperate help with this question!

(x^3-13x-18)/(x-4)

****** x^2 + 4 x + 3

(x-4)| x^3 + 0x^2 -13 x - 18
****** x^3 - 4x^2
*********** +4x^2 -13 x - 18
*********** +4x^2 -16 x
***************** +3 x - 18
***************** +3 x - 12
R = -6

SEE ALL THE DETAILS HERE:

http://calc101.com/webMathematica/long-divide.jsp

I'd be happy to help you with that question! To solve this problem, we need to divide the polynomial expression (x^3 - 13x - 18) by the linear expression (x - 4) using polynomial long division.

Here's a step-by-step guide on how to do it:

Step 1: Write down the dividend (x^3 - 13x - 18) and the divisor (x - 4) in the long division format. Fill in the placeholder for the quotient (which we'll find) above the dividend:

__________________
x - 4 | x^3 - 13x - 18

Step 2: Divide the first term of the dividend (x^3) by the first term of the divisor (x) to get the first term of the quotient. Write that term above the line:

__________________
x - 4 | x^3 - 13x - 18
x

Step 3: Multiply the divisor (x - 4) by the first term of the quotient (x), and write the result below the dividend:

x^2 - 4x
_____________
x - 4 | x^3 - 13x - 18
x

Step 4: Subtract the result obtained in step 3 from the dividend, and write the difference below the line:

x^3 - 13x - 18
- (x^2 - 4x)
_____________
x^3 - x^2 - 9x - 18

Step 5: Bring down the next term of the dividend. In this case, there is no term left, so we have the final difference:

x^3 - x^2 - 9x - 18

Step 6: Repeat steps 2 to 5 with the new difference. Divide the first term of the new difference (x^3 - x^2) by the first term of the divisor (x) to get the next term of the quotient. Write that term above the line:

__________________
x - 4 | x^3 - x^2 - 9x - 18
x - 1

Step 7: Multiply the divisor (x - 4) by the new term of the quotient (x - 1), and write the result below the previous difference:

x^2 - 4x
_____________
x - 4 | x^3 - x^2 - 9x - 18
x - 1
x^2 - 4x

Step 8: Subtract the result obtained in step 7 from the previous difference, and write the new difference below the line:

x^3 - x^2 - 9x - 18
- (x^2 - 4x)
_____________
3x - 18

Step 9: Bring down the next term of the new difference. In this case, we have 3x:

x^3 - x^2 - 9x - 18
- (x^2 - 4x)
_____________
3x - 18

Step 10: Divide the new term (3x) by the divisor (x - 4) to get the final term of the quotient. Write that term above the line:

__________________
x - 4 | x^3 - x^2 - 9x - 18
x - 1 + 3/(x - 4)

Step 11: Since there are no more terms left in the dividend, we have completed the long division process. The final answer is:

x^3 - 13x - 18 = (x - 1)(x - 4) + 3/(x - 4)

Therefore, the quotient is (x - 1) and the remainder is 3/(x - 4).

I hope this explanation helps you understand how to divide the given polynomial expression by the linear expression! Let me know if you have any further questions.