(x2+7x+12)÷(x+4)

Jasonbradley

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Jun 17, 2024

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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:

1. Set up the division:

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

2. 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.

3. Multiply the divisor:

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

4. Subtract:

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

5. Bring down the next term:

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

6. Repeat steps 2-5:

   • 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.