High School

Complete the synthetic division problem below:

Divide \(-3\) by the polynomial \(2x^2 + 4x - 4\).

What is the quotient in polynomial form?

Answer :

Final answer:

To complete the synthetic division problem for -3 / 2 4 -4 6, we use synthetic division steps, and the quotient in polynomial form is 2x² - 2x + 2.

Explanation:

To complete the synthetic division problem given by -3 / 2 4 -4 6, we follow the steps of synthetic division by using -3 as the divisor and 2, 4, -4, 6 as the coefficients of the polynomial we're dividing. The process is as follows:

  • Bring down the leading coefficient (2) to the bottom row.
  • Multiply this number by the divisor (-3) and place the result under the next coefficient (4).
  • Add the numbers in the second column to get the new number for the bottom row.
  • Continue this process until all coefficients have been used.

The result is 2 4 -4 6.

2 -6 6 -6

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2 -2 2 0

The quotient in polynomial form is 2x² - 2x + 2.