Add, Subtract & Multiply Polynomials Practice

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 does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of their degrees. For example, 7x^3 - 11x^2 + 8x - 5 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 expression. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

Front

How do you add polynomials?

Back

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

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 4) = (5 - 2)x^2 + (3 - 4) = 3x^2 - 1.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property or the FOIL method. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the square of a binomial?

Back

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

Front

What is the area of a rectangle represented by a polynomial?

Back

The area of a rectangle can be represented by the product of its length and width, which can be expressed as a polynomial. For example, if length = (2x + 3) and width = (x + 1), then area = (2x + 3)(x + 1) = 2x^2 + 5x + 3.

Front

What is a like term in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term in the polynomial. For example, 3x(2x^2 + 4x + 5) = 6x^3 + 12x^2 + 15x.