Polynomial Equations

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What is a polynomial equation?

Back

A polynomial equation is an equation that involves a polynomial expression, which is a sum of terms, each consisting of a variable raised to a non-negative integer power and multiplied by a coefficient.

Front

Identify the degree of the polynomial: x^3 + 2x^2 - x + 5.

Back

The degree of the polynomial is 3, which is the highest power of the variable x.

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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, such as ax^n + bx^(n-1) + ... + k.

Front

What is a linear polynomial?

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A linear polynomial is a polynomial of degree 1, which can be expressed in the form ax + b, where a and b are constants.

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What is a quadratic polynomial?

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A quadratic polynomial is a polynomial of degree 2, which can be expressed in the form ax^2 + bx + c, where a, b, and c are constants.

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What is a cubic polynomial?

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A cubic polynomial is a polynomial of degree 3, which can be expressed in the form ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

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How do you simplify the polynomial equation 3x^2 + 2x - 5 = 0?

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To simplify, you can rearrange it to the form 3x^2 + 2x = 5.

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What are the roots of a polynomial?

Back

The roots of a polynomial are the values of the variable that make the polynomial equal to zero.

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What is the Factor Theorem?

Back

The Factor Theorem states that if a polynomial f(x) has a root at x = r, then (x - r) is a factor of f(x).