Solving Polynomial Equations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x.

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is the degree of a polynomial?

Back

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

Front

What does it mean if a polynomial has an even degree?

Back

If a polynomial has an even degree, its ends will rise or fall in the same direction as x approaches positive or negative infinity.

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What does it mean if a polynomial has an odd degree?

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If a polynomial has an odd degree, its ends will rise in one direction and fall in the other as x approaches positive or negative infinity.

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What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n roots (including complex roots and multiplicities).

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What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial.

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What is the Rational Root Theorem?

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The Rational Root Theorem provides a way to find all possible rational roots of a polynomial equation.