-divided-by-(2x%2B3).jpeg "(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.