Which statement best justifies whether (x-3) is a factor of the polynomial p(x)=x3-3x2-2x-6?

1 answer:

3 0

The polynomial P(3) is not equal to zero, hence the function x - 3 is not a factor of the polynomial function given

Given the polynomial function of degree 3 expressed as

p(x) =x³-3x²-2x-6

In order to determine whether x - 3 is a factor, we will follow the simple steps below;

Let r(x) = x- 3

Since x - 3 is a factor, hence r(x) = 0]

x - 3 = 0

]x = 3

Substitute x = 3 into the polynomial function to see if p(3) = 0

P(3) = x³-3x²-2x-6

P(3) = 3³-3(3)²-2(3)-6

P(3) = 27 - 27 - 6 - 6

P(3) = -6-6

P(3) = -12

Since the polynomial P(3) is not equal to zero, hence the function x - 3 is not a factor of the polynomial function given

Learn more here: brainly.com/question/19030198

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What book has the solution in it?

Drupady [299]

Answer:

Book 3

Step-by-step explanation:

So we have four statements:

1: Book 1 or Book 2

2: Book 3 or Book 4

3: Book 4

4: Not Book 3

We also have the condition that only 1 of the statements are correct, and more important, the other 3 are incorrect.

So it may be a bit difficult to see at first, but the solution, has to be book 3. The reason for this is if we assume statement 1, statement 2, or statement 3 is true, that would imply that the statement 4 is false, meaning the solution is in book 3.

If we assume that statement 2 is true, then statement 4 is false, meaning that book 3 has the solution, which aligns statement 2. It also aligns with statement 1 being false, because it's not book 1 or 2, and it also aligns with statement 3 being false, because the solution is not in book 4.

Let's look at why assuming any other statement to be true, leads to contradictions.

So let's assume the first statement is true, this means the solution is book 1 or 2. But this means the statement 4 is false, meaning book 3 has the solution. This contradicts the first statement which we assume is true, thus the first statement is not true.

Let's now assume the third statement is true, this means statement four is false meaning it's book 3, but this contradicts the third statement which says it's book 4. Thus this statement cannot be true

Let's assume the last option is true, this means book 3 has no solution, and since all the other are false, book 4 has no solution, book 3 or 4 has no solution, book 1 or 2 has no solution either. This means that none of the books have solutions, and assuming one of the books does have a solution, this statement cannot be true.

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Find the probability of being dealt a full house. (Round your answer to six decimal places.)?

vesna_86 [32]

I'm assuming a 5-card hand being dealt from a standard 52-card deck, and that there are no wild cards.

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Suppose we fix both card values, say aces and 2s. We get a full house if we are dealt 2 aces and 3 2s, or 3 aces and 2 2s.

The number of ways of drawing 2 aces and 3 2s is

$\dbinom42\dbinom43=24$

and the number of ways of drawing 3 aces and 2 2s is the same,

$\dbinom43\dbinom42=24$

so that for any two card values involved, there are 2*24 = 48 ways of getting a full house.

Now, count how many ways there are of doing this for any two choices of card value. Of 13 possible values, we are picking 2, so the total number of ways of getting a full house for any 2 values is

$2\dbinom{13}2\dbinom42\dbinom43=3744$