Perform the indicated division
2x^2-7x-13/x-5
See:
http://www.purplemath.com/modules/polydiv2.htm
To perform the indicated division, you can use a method called polynomial long division. This method involves dividing the dividend (2x^2 - 7x - 13) by the divisor (x - 5) step-by-step. Here's how you can do it:
Step 1: Start by writing the dividend (2x^2 - 7x - 13) inside a long division bracket, and the divisor (x - 5) outside the bracket.
_______________________
x - 5 | 2x^2 - 7x - 13
Step 2: Divide the first term of the dividend (2x^2) by the first term of the divisor (x). The result goes on top.
_______________________
x - 5 | 2x^2 - 7x - 13
2x
Step 3: Multiply the divisor (x - 5) by the result from the previous step (2x), and write the result below the dividend starting from the second term.
_______________________
x - 5 | 2x^2 - 7x - 13
2x^2 - 10x
Step 4: Subtract the result from the previous step (2x^2 - 10x) from the dividend.
_______________________
x - 5 | 2x^2 - 7x - 13
- (2x^2 - 10x)
____________
3x - 13
Step 5: Bring down the next term from the original dividend. In this case, bring down the -13.
_______________________
x - 5 | 2x^2 - 7x - 13
- (2x^2 - 10x)
____________
3x - 13
- 3x + 15
Step 6: Repeat steps 2 to 5 with the new dividend (3x - 13).
_______________________
x - 5 | 2x^2 - 7x - 13
- (2x^2 - 10x)
____________
3x - 13
- 3x + 15
_________
2
Step 7: Since there are no more terms to bring down, the division is complete. The final answer is the quotient, which is 2.
Therefore, the result of dividing 2x^2 - 7x - 13 by x - 5 is 2.