High School

Use long division or synthetic division to find the quotient and remainder when [tex]3x^4 - 2x^2 + x - 7[/tex] is divided by [tex]x + 3[/tex]. Show your work.

a) Quotient: [tex]3x^3 - 9x^2 + 25x - 76[/tex], Remainder: 215

b) Quotient: [tex]3x^3 - 9x^2 + 24x - 70[/tex], Remainder: -175

c) Quotient: [tex]3x^3 - 9x^2 + 26x - 80[/tex], Remainder: 255

d) Quotient: [tex]3x^3 - 9x^2 + 27x - 84[/tex], Remainder: -295

Answer :

Final answer:

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.

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.

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