Adding, Subtracting, and Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 3x^2 + 2x + 1 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power. For example, (2x + 3) + (4x + 5) = 6x + 8.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves subtracting the coefficients of like terms. For example, (5x^2 + 3x) - (2x^2 + x) = 3x^2 + 2x.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. For example, (2x)(3x) = 6x^2.

Front

What is a like term?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

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 + 5, the degree is 3.

Front

What is the coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in the term 7x^2, 7 is the coefficient.

Front

What is the result of (3c^2)(10c^7)?

Back

The result is 30c^9.

Front

What is the result of subtracting (2a^2 + 5a + 3) - (a^2 - 3a - 4)?

Back

The result is a^2 + 8a + 7.

Front

What is the process of combining like terms?

Back

Combining like terms is the process of adding or subtracting coefficients of terms that have the same variable and exponent.