Find the quotient when (x^2-3x-4) is divided by (x+1).
Hey, that looks like the last one I did
(x+1)(x-4) / (x+1) = x-4
To find the quotient when dividing a polynomial by another polynomial, we can use the long division method.
Step 1: Write the dividend (x^2 - 3x - 4) and the divisor (x + 1) in long division format:
______
x + 1 | x^2 - 3x - 4
Step 2: Divide the term at the highest power of x in the dividend (x^2) by the term at the highest power of x in the divisor (x). Write the result above the line:
x
Step 3: Multiply the divisor (x + 1) by the quotient term you just found (x). Write the result below the dividend, aligning the terms with similar exponents:
x^2 + x
Step 4: Subtract the result in Step 3 from the dividend (x^2 - 3x - 4) and write the difference below the line:
______
x + 1 | x^2 - 3x - 4
- (x^2 + x)
-4x - 4
Step 5: Bring down the next term from the dividend (in this case, -4) and place it after the subtracted term:
______
x + 1 | x^2 - 3x - 4
- (x^2 + x)
___________
-4x - 4
- 4x - 4
Step 6: Repeat steps 2-5 using the new expression (-4x - 4) as the dividend.
Step 7: Divide the term at the highest power of x in the new dividend (-4x) by the term at the highest power of x in the divisor (x). Write the result above the line:
x - 4
Step 8: Multiply the divisor (x + 1) by the new quotient term (x - 4). Write the result below the line:
______
x + 1 | x^2 - 3x - 4
- (x^2 + x)
___________
-4x - 4
- ( -4x + 4)
___________
- 8
Step 9: Since the new dividend (-8) does not have any x term, we are done with the long division.
Therefore, the quotient when (x^2 - 3x - 4) is divided by (x + 1) is x - 4.