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

1. We can conclude that the result of the division is $x-13$ with a remainder of $4x-9$, or in other notation: $x-13+ \frac{4x-9}{x^2+3}$. 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: $x^{2}+6x+3+ \frac{2}{x-1}$. 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: $x+1+ \frac{5}{x-4}$. 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.