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TiliK225 [7]
2 years ago
6

Part A- Create a fourth degree polynomial in standard form. How do you know it is in standard form?

Mathematics
1 answer:
Alexeev081 [22]2 years ago
7 0

Answer:

(a)2x^4-9x^3+x^2+x-5

Step-by-step explanation:

(a)The degree of a polynomial is the highest power of the unknown variable in the polynomial.

A polynomial is said to be in standard form when it is arranged in descending order/powers of x.

An example of a fourth degree polynomial is: 2x^4-9x^3+x^2+x-5

We know the polynomial above is in standard form because it is arranged in such a way that the powers of x keeps decreasing.

(b)Polynomials are closed with respect to addition and subtraction. This is as a result of the fact that the powers do not change. Only the coefficients

change. This is illustrated by the two examples below:

(2x^5-3x^2+x)+(3x^5-5x^2)\\=2x^5-3x^2+x+3x^5-5x^2\\=5x^5-8x^2+x\\$Similarly\\(2x^5-3x^2+x)-(3x^5-5x^2)\\=2x^5-3x^2+x-3x^5+5x^2\\=-x^5+2x^2+x

The degrees do not change in the above operations. Only the number beside each variable changes. Therefore, the addition and subtraction of polynomials is closed.

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