PCX Chapter 2 FE Review

Front

What are the possible rational roots of a polynomial?

Back

The possible rational roots of a polynomial can be found using the Rational Root Theorem, which states that any rational solution, expressed as a fraction p/q, has p as a factor of the constant term and q as a factor of the leading coefficient.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor of the form (x - c). It is quicker and involves less writing than traditional long division.

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What is the significance of a zero placeholder in synthetic division?

Back

A zero placeholder is necessary in synthetic division to account for missing degrees of the polynomial. It ensures that the division process accurately reflects the polynomial's structure.

Front

What does 'multiplicity' of a root mean?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. A root with a multiplicity greater than 1 indicates that the graph of the polynomial touches the x-axis at that root.

Front

How do you write a polynomial in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of degree, from the highest degree to the lowest, with coefficients in front of each term.

Front

What is the relationship between the roots and the factors of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero. Each root corresponds to a factor of the polynomial in the form (x - root).

Front

How do you find the roots of a polynomial function?

Back

To find the roots of a polynomial function, you can use methods such as factoring, synthetic division, or applying the quadratic formula for quadratic polynomials.

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution of a polynomial equation can be expressed as a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

What is the process of factoring a polynomial?

Back

Factoring a polynomial involves rewriting it as a product of its factors, which can include linear factors and irreducible polynomials. This process helps in finding the roots of the polynomial.

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What is the role of the leading coefficient in a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the end behavior of the polynomial's graph.