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

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, in the expression 3x^2 + 5x^2, both terms are like terms because they both contain x^2.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 5x = (3 + 5)x = 8x.

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

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

How do you simplify the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

Combine like terms: 4a^3 + 7a^3 - 4a^2 - 8a - 6a - 7 = 11a^3 - 4a^2 - 14a - 7.

Front

What is the result of adding (4x - 2x^3) + (5x^3 - 4x + 5)?

Back

Combine like terms: -2x^3 + 5x^3 + 4x - 4x + 5 = 3x^3 + 5.

Front

How do you add the polynomials (2x + 5y - z) and (-6x - 4y + 7z)?

Back

Combine like terms: 2x - 6x + 5y - 4y - z + 7z = -4x + y + 6z.

Front

Ethan has (4x^3 - 5x^2 + 3x) and (-2x^3 - x^2 + 6x) apples. How many does he have in total?

Back

Combine like terms: (4x^3 - 2x^3) + (-5x^2 - x^2) + (3x + 6x) = 2x^3 - 6x^2 + 9x.

Front

What is the simplified form of (5x + 2) + (4x + 5)?

Back

Combine like terms: 5x + 4x + 2 + 5 = 9x + 7.