Adding and subtracting Polynomials 1

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 + 1 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. Like terms are terms that have the same variable raised to the same power.

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

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 + 4x = (3 + 4)x = 7x.

Front

What is the result of adding (3x^2 + 2x + 1) + (2x^2 - 4x - 5)?

Back

The result is 5x^2 - 2x - 4 after combining like terms.

Front

What is the result of subtracting (2x^3 - 5x^2 + 3x) - (-2x^3 - x^2 + 6x)?

Back

The result is 4x^3 - 4x^2 - 3x after distributing the negative sign and combining like terms.

Front

What is the formula for subtracting polynomials?

Back

To subtract polynomials, change the sign of each term in the polynomial being subtracted and then add the resulting polynomial to the first polynomial.

Front

What is the result of combining the like terms in 8x^3y + 3x^2y + 4xy + 5x^2y + 2xy + 7x^2y?

Back

The result is 8x^3y + 15x^2y + 6xy.

Front

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

Back

The result is -2x^3 + x^2 + 1 after combining 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 polynomial. For example, in 4x^3 + 2x^2 + 1, the degree is 3.