Polynomials Test Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^2 + 3x + 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 expression. For example, in the polynomial 4x^3 + 2x^2 + 7, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 5.

Front

What is the process of multiplying polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in one polynomial by each term in the other.

Front

What is the result of (x + 2)(x + 3)?

Back

The result is x^2 + 5x + 6.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is equal to a^2 + 2ab + b^2. For example, (3x - 2)^2 = 9x^2 - 12x + 4.

Front

How do you factor a polynomial?

Back

To factor a polynomial, find the greatest common factor (GCF) and use techniques like grouping or applying special formulas (e.g., difference of squares).

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as 5x^3 or -2.

Front

What is the result of -x^3(9x^4 - 2x^3 + 7)?

Back

The result is -9x^7 + 2x^6 - 7x^3.

Front

How do you divide a polynomial by a monomial?

Back

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. For example, (15x^9 - 8x^3) ÷ 3x^3 = 5x^6 - rac{8}{3}.