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)

1. We can conclude that the result of the division is [tex]x-13[/tex] with a remainder of [tex]4x-9[/tex], or in other notation: [tex]x-13+ \frac{4x-9}{x^2+3} [/tex]. Check the steps in the first image.

3. We can conclude that the result of the division is [tex]x^{2} +6x+3[/tex] with a remainder of 2, or in other notation: [tex] x^{2}+6x+3+ \frac{2}{x-1}[/tex]. Check the steps in the firts image.

5. We can conclude that the result of the division is [tex]x+1[/tex] with a remainder of 5, or in other notation: [tex]x+1+ \frac{5}{x-4}[/tex]. Check the steps in the first image.

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

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

10. We can conclude that the result of the synthetic division is [tex]-2x^{2}+9x+5[/tex]. Check the steps in the fourth image.