(9x^4+0x^3+8x^2+17x-20)÷(-3x-4)
In google type:
polynomials divided solver
When you see list of results click on:
calc101com/webMathematica/longdivide.jsp
When page be open in rectacangle Divide type:
9x^4+0x^3+8x^2+17x-20
In rectacangle by type:
-3x-4
Then click option DO IT
You will see solution.
Final answer is:
-3x^3+4x^2-8x+5
To divide the polynomial (9x^4 + 0x^3 + 8x^2 + 17x - 20) by (-3x - 4), you can use long division. Here's a step-by-step explanation of the process:
Step 1: Arrange the terms in descending order of exponents:
9x^4 + 0x^3 + 8x^2 + 17x - 20 divided by -3x - 4.
Step 2: Divide the first term of the dividend (9x^4) by the first term of the divisor (-3x). The result is (-3x^3).
Step 3: Multiply the entire divisor (-3x - 4) by the result from Step 2 (-3x^3). The result is (-9x^4 + 12x^3).
Step 4: Subtract the result from Step 3 from the dividend (9x^4 + 0x^3 + 8x^2 + 17x - 20) to get the new dividend:
(9x^4 + 0x^3 + 8x^2 + 17x - 20) - (-9x^4 + 12x^3) = (18x^3 + 8x^2 + 17x - 20).
Step 5: Bring down the next term from the original dividend. In this case, it is 8x^2.
Step 6: Repeat Steps 2-5 with the new dividend from Step 4 (18x^3 + 8x^2 + 17x - 20) and the original divisor (-3x - 4).
Step 2: Divide the first term of the new dividend (18x^3) by the first term of the divisor (-3x). The result is (-6x^2).
Step 3: Multiply the entire divisor (-3x - 4) by the result from Step 2 (-6x^2). The result is (18x^3 + 24x^2).
Step 4: Subtract the result from Step 3 from the new dividend (18x^3 + 8x^2 + 17x - 20) to get the new dividend:
(18x^3 + 8x^2 + 17x - 20) - (18x^3 + 24x^2) = (-16x^2 + 17x - 20).
Step 5: Bring down the next term from the original dividend. In this case, it is 17x.
Step 6: Repeat Steps 2-5 with the new dividend from Step 4 (-16x^2 + 17x - 20) and the original divisor (-3x - 4).
Step 2: Divide the first term of the new dividend (-16x^2) by the first term of the divisor (-3x). The result is (5x).
Step 3: Multiply the entire divisor (-3x - 4) by the result from Step 2 (5x). The result is (-15x^2 - 20x).
Step 4: Subtract the result from Step 3 from the new dividend (-16x^2 + 17x - 20) to get the new dividend:
(-16x^2 + 17x - 20) - (-15x^2 - 20x) = (x^2 + 37x - 20).
Step 5: Bring down the next term from the original dividend. In this case, it is -20.
Step 6: Repeat Steps 2-5 with the new dividend from Step 4 (x^2 + 37x - 20) and the original divisor (-3x - 4).
Step 2: Divide the first term of the new dividend (x^2) by the first term of the divisor (-3x). The result is (-1/3x).
Step 3: Multiply the entire divisor (-3x - 4) by the result from Step 2 (-1/3x). The result is (x^2 + 4/3x).
Step 4: Subtract the result from Step 3 from the new dividend (x^2 + 37x - 20) to get the remainder:
(x^2 + 37x - 20) - (x^2 + 4/3x) = (37x - 20 - 4/3x).
The remainder is (37x - 20 - 4/3x).
Therefore, the quotient is (-3x^3 - 6x^2 + 5x - 1/3) and the remainder is (37x - 20 - 4/3x).