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# How do you write a polynomial in standard form?

A:

Writing a polynomial in standard form means putting the term with the highest exponent first. The other terms with lower exponents are written in descending order.

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An example of a polynomial in standard form is x^8 + 2 x^6 + 4 x^3 + 2x^2 + 3x - 2. In this example, there are terms with exponents and a constant. In the given polynomial, "x" is a variable, and the term "x^8" has the highest exponent, which is 8. This is also called the degree of the polynomial. The next term that follows is "2x ^6," which has the lower exponent of 6. The other terms in this polynomial are in descending order when looking at the exponents.

When writing a polynomial in standard form, it is important to look at each term to identify the exponents from highest to lowest correctly. The constant term, a number by itself, goes last in the standard form of polynomials.

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Many linear equations are given in slope-intercept form (y = mx + b), and sometimes they must be converted to standard form (Ax + By = C). Converting slope-intercept to standard form is mostly a matter of converting fractions to integers and can be done on paper in a couple minutes.

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Factoring completely is an algebraic process that incorporates the three common factoring techniques: the greatest common factor, trinomials and the difference between two squares. These techniques by themselves often factor a polynomial into a single pattern, while factoring completely utilizes them together to simplify an expression as much as possible.

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A monic polynomial is a mathematical expression that consists of coefficients and a single variable, with the leading coefficient equal to one. The leading coefficient is found in the term that contains the variable with the highest degree or exponent.