More Algebra 2 problems.

*January 2018*
*19. If p(x) = 2x ^{3} - 3x + 5, what is the remainder of p(x) : (x - 5)?
(1) -230
(2) 0
(3) 30
(4) 240
*

**Answer: (4) 240**

The Polynomial Remainder Theorem tells us that is p(x) is divided by (x - r), then the remainder, R, can be found by evaluating p(r).

If (x - 5) is a factor of p(x), then when x = 5, p(x) would = 0. If it is not a factor, then the value of p(5) will be the remainder when you divide the polynomials.

If you calculate p(5), you will get 2(5)^{3} - 3(5) + 5 = 240, which is the remainder.

Alternatively, if you forgot this, you can do the polynomial division. This will give you 240 as a remainder. See the image below:

*20. The results of simulating tossing a coin 10 times, recording the number of heads, and repeating this 50 times are shown in the graph below.*

Based on the results of the simulation, which statement is false?

(1) Five heads occurred most often, which is consistent with the theoretical probability of obtaining a heads.

(2) Eight heads is unusual, as it falls outside the middle 95% of the data.

(3) Obtaining three heads or fewer occurred 28% of the time.

(4) Seven heads is not unusual, as it falls within the middle 95% of the data.

Based on the results of the simulation, which statement is false?

(1) Five heads occurred most often, which is consistent with the theoretical probability of obtaining a heads.

(2) Eight heads is unusual, as it falls outside the middle 95% of the data.

(3) Obtaining three heads or fewer occurred 28% of the time.

(4) Seven heads is not unusual, as it falls within the middle 95% of the data.

**Answer: (2) Eight heads is unusual, as it falls outside the middle 95% of the
data.**

Eight does not fall outside the middle 95% of the data. There are 50 data points, so 47.5 pieces of data are in the middle, leaving 2.5 / 2 = 1.25 pieces of data more than two standard deviations above and below the mean. But there are two results greater than 8, so it's not outside of the middle 95%.

Comments and questions welcome.

More Algebra 2 problems.

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