Dividing Polynomials: (x² + 7x + 12) ÷ (x + 4)
This article will guide you through the process of dividing the polynomial (x² + 7x + 12) by (x + 4) using polynomial long division.
Polynomial Long Division
Polynomial long division is a method for dividing polynomials similar to the long division method used for integers. Here's how it works:

Set up the division:
 Write the dividend (x² + 7x + 12) inside the division symbol.
 Write the divisor (x + 4) outside the division symbol.

Divide the leading terms:
 Divide the leading term of the dividend (x²) by the leading term of the divisor (x). This gives you x.
 Write x above the division symbol.

Multiply the divisor:
 Multiply the divisor (x + 4) by the quotient term (x) to get x² + 4x.
 Write this result below the dividend.

Subtract:
 Subtract x² + 4x from the dividend. This leaves you with 3x + 12.

Bring down the next term:
 Bring down the next term of the dividend (12) to form the new expression 3x + 12.

Repeat steps 25:
 Divide the leading term of the new expression (3x) by the leading term of the divisor (x) to get 3.
 Multiply the divisor (x + 4) by 3 to get 3x + 12.
 Subtract this result from the expression, leaving 0.
Solution
Following these steps, the long division looks like this:
x + 3
x + 4  x² + 7x + 12
(x² + 4x)

3x + 12
(3x + 12)

0
Therefore, (x² + 7x + 12) ÷ (x + 4) = x + 3.
Conclusion
Polynomial long division is a valuable tool for dividing polynomials. By systematically dividing the dividend by the divisor, we can find the quotient and remainder. In this case, we found that the quotient of (x² + 7x + 12) ÷ (x + 4) is x + 3.