divide -2x^3+21x^2-20x-12 by (x-3)
drop in at calc101.com and click on the long division link.
It will show the division in detail
you can compare that with doing synthetic division.
thanks for the site
To divide the polynomial -2x^3 + 21x^2 - 20x - 12 by (x-3), you can use the long division method. Here's a step-by-step explanation:
Step 1: Write the polynomial in descending order of exponents:
-2x^3 + 21x^2 - 20x - 12
Step 2: Identify the highest power of x in the dividend and the divisor. In this case, the highest power of x is x^3.
Step 3: Divide the first term of the dividend by the first term of the divisor. In this case, divide -2x^3 by (x - 3). The result is -2x^2.
Step 4: Multiply the divisor by the result obtained in step 3 (-2x^2) and write the product below the dividend, aligned with the matching term. Here, -2x^2 * (x - 3) is -2x^3 + 6x^2.
Step 5: Subtract the product obtained in step 4 from the dividend. -2x^3 + 21x^2 - 20x - 12 - (-2x^3 + 6x^2) simplifies to 15x^2 - 20x - 12.
Step 6: Bring down the next term of the dividend. In this case, bring down 15x^2.
Step 7: Repeat steps 3 to 6. Divide the first term of the new dividend (15x^2) by the first term of the divisor (x - 3). The result is 15x.
Step 8: Multiply the divisor by the result obtained in step 7 (15x) and write the product below the new dividend. Here, 15x * (x - 3) is 15x^2 - 45x.
Step 9: Subtract the product obtained in step 8 from the new dividend. 15x^2 - 20x - 12 - (15x^2 - 45x) simplifies to 25x - 12.
Step 10: If there are no more terms left in the dividend to bring down, the process is complete. The quotient is the result of all the division steps. Here, the quotient is -2x^2 + 15x + 5.
Therefore, the division of -2x^3 + 21x^2 - 20x - 12 by (x - 3) is equal to -2x^2 + 15x + 5.