Operations of Polynomials

Front

Define a polynomial.

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, 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

Simplify: (2n^2 - 8n^4) + (4n^2 - 5n^4)

Back

-13n^4 + 6n^2

Front

What is the result of subtracting two polynomials?

Back

The result is obtained by subtracting the coefficients of like terms.

Front

Simplify: (7x - 3y - 9z) - (5x + y - 4z)

Back

2x - 4y - 5z

Front

Find the sum: (3x^3 + 3x^2 - 4x + 5) + (x^3 - 2x^2 + x - 4)

Back

4x^3 + 1x^2 - 3x + 1

Front

What is the process of adding polynomials?

Back

To add polynomials, combine like terms by adding their coefficients.

Front

Simplify: (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)

Back

11x^4 + 2x^2 + 14x

Front

What is the distributive property in polynomial multiplication?

Back

The distributive property states that a(b + c) = ab + ac, which applies to multiplying polynomials.

Front

Multiply: (2x + 3)(x - 2)

Back

2x^2 - x - 6