%2F(x-3)-long-division.jpeg "(x^2-x-6)/(x-3) Long Division")
Long Division of Polynomials: (x^2 - x - 6) ÷ (x - 3)
Long division of polynomials is a method used to divide one polynomial by another. It's similar to the long division you learned in elementary school, but it involves variables and exponents. Here's how to perform the long division of (x^2 - x - 6) ÷ (x - 3):
Step 1: Set up the division problem
Write the dividend (x^2 - x - 6) inside the division symbol and the divisor (x - 3) outside.
_______
x - 3 | x^2 - x - 6
Step 2: Divide the leading terms
- Divide the leading term of the dividend (x^2) by the leading term of the divisor (x). This gives you x.
- Write the result (x) above the division symbol.
x ______
x - 3 | x^2 - x - 6
Step 3: Multiply the divisor by the quotient
- Multiply the divisor (x - 3) by the quotient (x). This gives you x^2 - 3x.
- Write the result below the dividend.
x ______
x - 3 | x^2 - x - 6
x^2 - 3x
Step 4: Subtract
- Subtract the result from the dividend. This gives you 2x.
- Bring down the next term of the dividend (-6).
x ______
x - 3 | x^2 - x - 6
x^2 - 3x
--------
2x - 6
Step 5: Repeat steps 2-4
- Divide the new leading term of the dividend (2x) by the leading term of the divisor (x). This gives you 2.
- Write the result (2) above the division symbol.
x + 2 ______
x - 3 | x^2 - x - 6
x^2 - 3x
--------
2x - 6
- Multiply the divisor (x - 3) by the quotient (2). This gives you 2x - 6.
- Write the result below the dividend.
x + 2 ______
x - 3 | x^2 - x - 6
x^2 - 3x
--------
2x - 6
2x - 6
- Subtract the result from the dividend. This gives you 0.
x + 2 ______
x - 3 | x^2 - x - 6
x^2 - 3x
--------
2x - 6
2x - 6
-------
0
Step 6: The answer
Since the remainder is 0, the division is complete. The quotient is x + 2.
Therefore, (x^2 - x - 6) ÷ (x - 3) = x + 2.