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tiny-mole [99]
3 years ago
12

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)

Mathematics
1 answer:
artcher [175]3 years ago
3 0
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. 

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