Test on Polynomials

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, 3x^2 + 2x - 5 is a polynomial.

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 the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3x^2 + 4x) + (2x^2 + 5) = (3x^2 + 2x^2) + 4x + 5 = 5x^2 + 4x + 5.

Front

What is a constant polynomial?

Back

A constant polynomial is a polynomial of degree 0, which means it has no variable term. For example, the polynomial 12 is a constant polynomial.

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. For example, 2x + 3 is a linear polynomial.

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. For example, x^2 - 4x + 4 is a quadratic polynomial.

Front

What is the product of (5x + 1)(x + 4)?

Back

The product is 5x^2 + 21x + 4.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 4x - 2) - (5x + 7) = 3x^2 + 4x - 2 - 5x - 7 = 3x^2 - x - 9.

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. For example, x^3 - 2x^2 + 3x - 1 is a cubic polynomial.

Front

What does it mean to simplify a polynomial?

Back

Simplifying a polynomial means combining like terms and reducing the expression to its simplest form. For example, simplifying 6b^3 + 6 - b^4 - (8b^3 - 6b^4 + 2) results in 5b^4 - 2b^3 + 4.