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SSSSS [86.1K]
3 years ago
10

What is the remainder R when the polynomial p(x) is divided by (x - 2)? Is (x - 2) a factor of p(x)? P(x) = -4x4 + 6x3 + 8x2 - 6

x - 4 A) R = 0, no B) R = 0, yes C) R = -72, no D) R = -72, yes
Mathematics
1 answer:
Trava [24]3 years ago
7 0

Answer:

B

(x-2) is a factor since remainder is 0.

Step-by-step explanation:

We divide (x-2) into the polynomial -4x^4+6x^3+8x^2-6x-4 through long division or synthetic. We choose long division and look for what will multiply with (x-2) to make the polynomial -4x^4+6x^3+8x^2-6x-4 .

(x-2)(-4x^3)=-4x^4+8x^3

We subtract this from the original -4x^4-(-4x^4)+6x^3-(8x^3)+8x^2-6x-4.

This leaves -2x^3+8x^2-6x-4. We repeat the step above.

(x-2)(-2x^2)=-2x^3+4x^2.

We subtract this from -2x^3-(-2x^3)+8x^2-(4x^2)-6x-4=4x^2-6x-4. We repeat the step above.

(x-2)(4x)=4x^2-8x.

We subtract this from 4x^2-(4x^2)-6x-(-8x)-4=2x-4. We repeat the step above.

(x-2)(2)=2x-4.

We subtract this from 2x-(2x)-4-(4)=0. There is no remainder. This means (x-2) is a factor.


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Answer:

Step-by-step explanation:

Average rate of change is the same thing as the slope. This is a quadratic so the slope is not something that is constant like it is in a line. Here you have the x coordinates of 1 and 5; each one of these x coordinates has a y coordinate that goes with it. If we draw a line from one of these coordinates to another,  that line will have a slope. That is the slope we are trying to find. Thus, we need the y coordinates that go with each of these x coordinates. To do that, plug x into the equation and do the math to find y:

Let's start with x = 1.

f(1) = 17-(1)^2 so

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3 years ago
An art history professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below
madam [21]

Answer:

The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4.

This means that \mu = 79.7, \sigma = 8.4

B: Scores below the top 13% and above the bottom 56%

So between the 56th percentile and the 100 - 13 = 87th percentile.

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X when Z has a p-value of 0.56, so X when Z = 0.15. Then

Z = \frac{X - \mu}{\sigma}

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X - 79.7 = 0.15*8.4

X = 81

87th percentile:

X when Z has a p-value of 0.87, so X when Z = 1.13.

Z = \frac{X - \mu}{\sigma}

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X - 79.7 = 1.13*8.4

X = 89

The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.

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