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Consider the polynomial 3x³ - 2x + 7.

1) How many terms does this polynomial have?
2) What is the coefficient of the second term?
1) The polynomial has five terms.
2) The coefficient of the second term is -2.
1) The polynomial has three terms.
2) The coefficient of the second term is -2.
1) The polynomial has three terms.
2) The coefficient of the second term is x.
1) The polynomial has five terms.
2) The coefficient of the second term is x.

1 Answer

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Answer:

(b) 1) The polynomial has three terms. 2) The coefficient of the second term is -2

Explanation:

You want the number of terms and the coefficient of the second term of the polynomial ...

3x³ - 2x + 7

Terms

The terms of a polynomial are products. Each product has factors that are one or more constants and one or more variables to some whole number power(s). We generally count terms from the left. In standard form, the terms are in order of decreasing degree.

1st term: 3x³ — coefficient = 3, degree (exponent) = 3

2nd term: -2x — coefficient: = -2, degree = 1

3rd term: 7 — coefficient: 7, degree = 0. This is also called a "constant term".

The polynomial has 3 terms. The coefficient of the 2nd term is -2.

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Additional comment

There is no degree 2 term in this polynomial as written. If you were to do polynomial division with this polynomial as the dividend, you would include a term 0x² as a place holder.

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