Perform the indicated division
2x^2-7x-13/x-5
To perform the division, we will use long division method. Here are the steps:
Step 1: Write the dividend (2x^2 - 7x - 13) and divisor (x - 5) in the division format:
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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), which gives us 2x.
Step 3: Multiply the divisor (x - 5) by the quotient (2x) and write the result below the dividend. We get:
2x * (x - 5) = 2x^2 - 10x.
Step 4: Subtract the result (2x^2 - 10x) from the dividend (2x^2 - 7x - 13). We get:
(2x^2 - 7x - 13) - (2x^2 - 10x) = (-7x + 10x - 13) = (3x - 13).
Step 5: Bring down the next term from the original dividend, which is -13.
The new dividend becomes (3x - 13).
Step 6: Repeat steps 2-5 with the new dividend (3x - 13) until we have no more terms to bring down.
In this case, we have no more terms left to bring down.
Step 7: Write the final result:
The quotient is 2x + 3.
The remainder is (3x - 13).
Therefore, the division of (2x^2 - 7x - 13) by (x - 5) is:
Quotient: 2x + 3
Remainder: 3x - 13