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lubasha [3.4K]
3 years ago
5

Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)

Mathematics
1 answer:
Svetlanka [38]3 years ago
4 0

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17. The polynomial is in standards when has the form p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}, where n is the order of the polynomial. The example has the following information:

n = 3, a_{0} = 17, a_{1} = -6, a_{2} = 2, a_{3} = 5.

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials p_{1} and p_{2} such that:

p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i} and p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}, where m \geq n

p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be p_{1} a polynomial such that:

p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}

And \alpha an scalar. If the polynomial is multiplied by the scalar number, then:

\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}

Lastly, the following expression is constructed by distributive property:

\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}

Hence, polynomials are closed with respect to multiplication.

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the answer is
a triangle’s enlargement dimensions will be 52.8 cm by 80 cm


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3 years ago
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Answer:

1/2

Step-by-step explanation:

might be wrong with this thinking, but since he already told you he has one boy you just need to look at the probablity that the other is a boy. each kid had a 50% chance. so the remaining kid of unknown gender has a 50% chance of being a boy.

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