Mon Dec 2.... Dividing Polynomials Flashcard

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^3 + 5x^2 + 9 is a polynomial.

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What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 5x^2 + 9, the degree is 3.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c). It is faster and requires less writing than long division.

Front

What is long division in polynomials?

Back

Long division in polynomials is a method used to divide a polynomial by another polynomial, similar to long division with numbers.

Front

How do you find the width of a rectangle if you know the area and one side?

Back

To find the width, divide the area by the known length. For example, if the area is x^2 + 14x + 40 and the length is x + 4, the width is (x^2 + 14x + 40) / (x + 4).

Front

What is the remainder theorem?

Back

The remainder theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

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What is the factor theorem?

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The factor theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 6x^4 - 4x^3 + 3x + 1.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 6x^4 - 4x^3 + 3x + 1, the leading coefficient is 6.

Front

What is the difference between a monomial and a polynomial?

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A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x is a monomial, while 3x + 2 is a polynomial.