Question

Divide using long division. check your answers. 1. (x 3 – 13x 2 + 7x – 48) ÷ (x 2 + 3) 3. (x 3 + 5x 2 – 3x – 1) ÷ (x – 1) 5. (x 2 – 3x + 1) ÷ (x – 4) determine whether each binomial is a factor of x 3 + 3x 2 – 10x – 24. 7. x + 4 9. x – 3 divide using synthetic division. 13. (–2x 3 + 15x 2 – 22x – 15) ÷ (x – 3)

Answer 1

yes

Step-by-step explanation: e e e

Answer 2

1. We can conclude that the result of the division is
`x-13` with a remainder of
`4x-9`, or in other notation:
`x-13+ (4x-9)/(x^2+3)`. Check the steps in the first image.

3. We can conclude that the result of the division is
`x^(2) +6x+3` with a remainder of 2, or in other notation:
`x^(2)+6x+3+ (2)/(x-1)`. Check the steps in the firts image.

5. We can conclude that the result of the division is
`x+1` with a remainder of 5, or in other notation:
`x+1+ (5)/(x-4)`. Check the steps in the first image.

7. To check if
`x+4` is a factor of
`x^(3)+3x^(2)-10x-24`, we are going to perform long division. If the result of the long division has no remainder,
`x+4` is a factor of
`x^(3)+3x^(2)-10x-24`.
Since the result of the long division has no remainder, we can conclude that
`x+4` is a factor of
`x^(3)+3x^(2)-10x-24`. Check the steps in the second image.

9. To check if
`x-3` is a factor of
`x^(3)+3x^(2)-10x-24`, we are going to perform long division. If the result of the long division has no remainder,
`x-4` is a factor of
`x^(3)+3x^(2)-10x-24`.
Since the result of the long division has no remainder, we can conclude that
`x-4` is a factor of
`x^(3)+3x^(2)-10x-24`. Check the steps in the third image.

10. We can conclude that the result of the synthetic division is
`-2x^(2)+9x+5`. Check the steps in the fourth image.