Question

Use long division or synthetic division to find the quotient and remainder when 3x⁴ - 2x² + x - 7 is divided by x + 3. Show your work.

a) Quotient: 3x³ - 9x² + 25x - 76, Remainder: 215
b) Quotient: 3x³ - 9x² + 24x - 70, Remainder: -175
c) Quotient: 3x³ - 9x² + 26x - 80, Remainder: 255
d) Quotient: 3x³ - 9x² + 27x - 84, Remainder: -295

Answer 1

To divide the polynomial 3x⁴ - 2x² + x - 7 by x + 3, use long division. The quotient is 3x³ - 9x² + 24x - 70 and the remainder is -175.

Step-by-step explanation:

To divide the polynomial 3x⁴ - 2x² + x - 7 by x + 3, we will use long division.

Here is the step-by-step process:

1. Start by dividing the first term of the polynomial, 3x⁴, by x.
2. This gives us 3x³.
3. Multiply the divisor, x + 3, by the quotient found in the previous step, 3x³.
4. This gives us 3x⁴ + 9x³.
5. Subtract this product from the original polynomial: (3x⁴ - 2x² + x - 7) - (3x⁴ + 9x³) = -9x³ - 2x² + x - 7.
6. Bring down the next term, which is -9x³.
7. Repeat the process until all terms have been divided.

After completing all the steps, we find that the quotient is 3x³ - 9x² + 24x - 70 and the remainder is -175.