(4x^2-10x-24) Divided By (2x+3)

4 min read Jun 16, 2024
(4x^2-10x-24) Divided By (2x+3)

Dividing Polynomials: (4x^2 - 10x - 24) ÷ (2x + 3)

This article will guide you through the process of dividing the polynomial (4x^2 - 10x - 24) by the binomial (2x + 3). We will use the long division method to solve this problem.

Step 1: Setting up the Long Division

Write the dividend (4x^2 - 10x - 24) inside the division symbol and the divisor (2x + 3) outside.

        _______
2x + 3 | 4x^2 - 10x - 24 

Step 2: Dividing the Leading Terms

Divide the leading term of the dividend (4x^2) by the leading term of the divisor (2x). This gives us 2x. Write this result above the division symbol.

        2x ______
2x + 3 | 4x^2 - 10x - 24 

Step 3: Multiplying the Quotient by the Divisor

Multiply the quotient (2x) by the divisor (2x + 3). This gives us 4x^2 + 6x. Write this below the dividend.

        2x ______
2x + 3 | 4x^2 - 10x - 24 
          4x^2 + 6x 

Step 4: Subtracting

Subtract the result (4x^2 + 6x) from the dividend (4x^2 - 10x - 24). Remember to change the signs of the terms you are subtracting.

        2x ______
2x + 3 | 4x^2 - 10x - 24 
          4x^2 + 6x 
          ---------
               -16x - 24 

Step 5: Bringing Down the Next Term

Bring down the next term of the dividend (-24).

        2x ______
2x + 3 | 4x^2 - 10x - 24 
          4x^2 + 6x 
          ---------
               -16x - 24 

Step 6: Repeat Steps 2-5

Repeat steps 2-5 with the new polynomial (-16x - 24).

  • Divide the leading term (-16x) by the leading term of the divisor (2x). This gives us -8. Write this next to the 2x in the quotient.
        2x - 8 ______
2x + 3 | 4x^2 - 10x - 24 
          4x^2 + 6x 
          ---------
               -16x - 24 
  • Multiply the quotient (2x - 8) by the divisor (2x + 3). This gives us -16x - 24. Write this below the -16x - 24.
        2x - 8 ______
2x + 3 | 4x^2 - 10x - 24 
          4x^2 + 6x 
          ---------
               -16x - 24 
               -16x - 24
  • Subtract the result (-16x - 24) from the dividend (-16x - 24).
        2x - 8 ______
2x + 3 | 4x^2 - 10x - 24 
          4x^2 + 6x 
          ---------
               -16x - 24 
               -16x - 24
               ---------
                     0

Conclusion

The result of the division is 2x - 8. This means (4x^2 - 10x - 24) divided by (2x + 3) equals 2x - 8.

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