Answer :

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The division of x³ - 7x² + 13x - 6 by x - 2 will have a quotient of x² - 5x + 3 and a remainder zero (0) using long division.

Dividing with long division

The procedure for long division involves the following steps:

  • Divide.
  • Multiply.
  • Subtract.
  • Bring down the next term, and
  • Repeat the process to get zero or arrive at a remainder.

We shall divide the x³ - 7x² + 13x - 6 by x - 2 as follows;

x³ divided by x equals x²

x - 2 multiplied by x² equals x² - 2x²

subtract x² - 2x² from x³ - 7x² + 13x - 6 will give us -5x² + 13x - 6

-5x² divided by x equals -5x

x - 2 multiplied by -5x equals -5x² + 10x

subtract -5x² + 10x from -5x² + 13x - 6 will give us 3x - 6

3x divided by x equals 3

x - 2 multiplied by 3 equals 3x - 6

subtract -3x - 6 from 3x - 6 will result to a remainder of zero (0)

Therefore, x³ - 7x² + 13x - 6 by x - 2 is equal to the quotient of x² - 5x + 3 with a remainder of 0.

Learn more about long division here: https://brainly.com/question/25289437

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