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lutik1710 [3]
1 year ago
8

Divide g(x) = x^4 - 2x^3 + X + 3 by x+3

Mathematics
1 answer:
SVEN [57.7K]1 year ago
8 0

Let's first get the coefficients of the numerator: x^4 - 2x^3 + x + 3 = 1, -2, 0, 1, 3

<em>There is no x^2 in the expression, thus, the coefficient for x^2 = 0</em>

Zero of the denominator: x + 3; x = -3

Using synthetic division,

-3 I 1 -2 0 1 3

I_________________

-3 I 1 -2 0 1 3

I_________________

1

-3 I 1 -2 0 1 3

I_____-3___________

1 -5

-3 I 1 -2 0 1 3

I_____-3__15_______

1 -5 15

-3 I 1 -2 0 1 3

I_____-3__15_-45____

1 -5 15 -44

-3 I 1 -2 0 1 3

I_____-3__15_-45____

1 -5 15 -44

-3 I 1 -2 0 1 3

I_____-3__15_-45_132__

1 -5 15 -44 135

The remainder is 135. Which transforms it into 135/x+3.

Thus, the quotient of x^4 - 2x^3 + x + 3 divided by x + 3 ​is:

x-5x^2+15x\text{ - 44 + }\frac{135}{x+3}

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Step-by-step explanation:

1/8 ×11= 11/8

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Find m∠ABC in the picture. (it's not solving for x.)
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The answer would be 6º

Step-by-step explanation:

first we know that a straight lin is always 180º

so since we know that the angle outside of the triangle is 110º we can do 180º -110º

then we get the measuerment for angle C :70º

since we dont know the measurements of the other angles but know that a full triangle is equal to 180º we make this equation

2+6x+12x+70=180

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3. This spinner is divided into eight equal-sized sections. Each section is labeled with a number
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Answer:

Least Likely: Arrow lands on a section labeled with an odd number.

_____: Arrow lands on a section labeled with the number 1.

Most Likely: Arrow lands on a section labeled with a number less than 4.

Step-by-step explanation:

<u>The spinner:</u>

There are 8 sections, 4 labeled with the number 1, 2 labeled with the number 3, 1 labeled with the number 3, and 1 labeled with the number 4.

<u>Probabilities of the spinner:</u>

  • Probability of landing on 1: 4/8 - 50%
  • Probability of landing on 2: 1/8 - 12.5%
  • Probability of landing on 3: 2/8 - 25%
  • Probability of landing on 4: 1/8 - 12.5%

<u>The options:</u>

A - Arrow lands on a section labeled with an odd number.

B - Arrow lands on a section labeled with the number 1.

C - Arrow lands on a section labeled with a number less than 4.

  1. The least likely possibility out of the options would be B because, while a 50% chance sounds like a lot, it is the least of the three options.
  2. The mid possibility out of the options would be A. The odd numbers labeled on the spinner make up 75% of the whole. (1s and 3s - 50% + 25%)
  3. The most likely possibility out of the options is C because it accounts for every section except for the single section labeled with the number 4. (100% - 12.5%, 87.5%)
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