Polynomials: Standard Form

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^2 + 3x - 5 is a polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 - 2x^2 + x - 7 is in standard form.

Front

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 5x^3 - 6x + 1, the degree is 3.

Front

Classify the polynomial 3x^4 - 2x^3 + x - 7 by its degree.

Back

Degree of 4.

Front

What is a linear polynomial?

Back

A linear polynomial is a polynomial of degree 1, which can be expressed in the form ax + b, where a and b are constants and a ≠ 0.

Front

What is a quadratic polynomial?

Back

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 and a ≠ 0.

Front

What is a cubic polynomial?

Back

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 and a ≠ 0.

Front

What is a quartic polynomial?

Back

A quartic polynomial is a polynomial of degree 4, which can be expressed in the form ax^4 + bx^3 + cx^2 + dx + e, where a, b, c, d, and e are constants and a ≠ 0.

Front

Is the polynomial 2x^2 + 3x - 5 in standard form?

Back

True.

Front

Is the polynomial \frac{6}{x^2}-5x+1 in standard form?

Back

False.