use polynomial long division to divide
4x^3+6x^2+16x-10 by -x^2-2x-5
help me please
a quick visit to calc101.com will show the steps involved to get
-4x+2
Sure, I can help you with polynomial long division. To divide the polynomial 4x^3+6x^2+16x-10 by -x^2-2x-5 using polynomial long division, you need to follow these steps:
Step 1: Arrange the terms of the dividend and divisor in descending order of their exponents.
The dividend is: 4x^3+6x^2+16x-10
The divisor is: -x^2-2x-5
Step 2: Divide the first term of the dividend by the first term of the divisor.
The first term of the dividend is 4x^3, and the first term of the divisor is -x^2. Their division is -4x.
Step 3: Multiply the entire divisor by the result obtained in Step 2, and write the product under the dividend.
Multiplying -4x with -x^2-2x-5, we get 4x^3 + 8x^2 + 20x.
Step 4: Subtract the result obtained in Step 3 from the dividend.
Subtracting (4x^3 + 8x^2 + 20x) from (4x^3 + 6x^2 + 16x - 10), we get -2x^2 - 4x - 10.
Step 5: Bring down the next term from the dividend.
Bringing down the next term, which is -10, we now have -2x^2 - 4x - 10.
Step 6: Repeat steps 2 to 5 until there are no more terms left in the dividend.
For the new dividend -2x^2 - 4x - 10 and the divisor -x^2-2x-5:
- Divide the first term of the new dividend, -2x^2, by the first term of the divisor, -x^2, to get 2x.
- Multiply 2x by the entire divisor (-x^2-2x-5), which gives -2x^3 - 4x^2 - 10x.
- Subtracting (-2x^3 - 4x^2 - 10x) from (-2x^2 - 4x - 10), we get -6x^2 + 6x.
- Bring down the next term, which is 6x.
- Repeat steps 2 to 5 with the new dividend -6x^2 + 6x and the same divisor -x^2-2x-5.
The process will continue until the dividend becomes a lower degree polynomial than the divisor or until there are no more terms left in the dividend.
Please let me know if you need help with the subsequent steps or if you have any further questions.