Polynomial Operations and Simplifications

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms.

Front

How do you simplify the expression (3x - 5)(4x^2 - 2x - 3)?

Back

The simplified expression is 12x^3 - 26x^2 + x + 15.

Front

How do you simplify the expression x^3(2x^2 + 3x)?

Back

The simplified expression is 2x^5 + 3x^4.

Front

What is the sum of (2x^2 + 5x - 7) + (3 - 4x^2 + 6x)?

Back

The sum is -2x^2 + 11x - 4.

Front

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

Back

The result is -21x^4 + 3x^3 - 12x^2.

Front

What is the process of combining like terms in polynomials?

Back

Combining like terms involves adding or subtracting coefficients of terms that have the same variable raised to the same power.