Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves taking one polynomial and removing the terms of another polynomial from it, which requires distributing the negative sign and combining like terms.

Front

How do you combine like terms in a polynomial?

Back

To combine like terms, identify terms that have the same variable raised to the same power and add or subtract their coefficients.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degree, from the highest degree to the lowest.

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

How do you simplify the expression (2x + 5y) - (3x - 2y)?

Back

To simplify, distribute the negative sign: 2x + 5y - 3x + 2y = -x + 7y.

Front

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

Back

The result is -5x^5 + 2x^3 - 6x.

Front

How do you handle subtraction when one polynomial has a higher degree than the other?

Back

When subtracting, ensure to align like terms and subtract coefficients accordingly, regardless of the degree.

Front

What is the result of (6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2)?

Back

The result is 5b^4 - 2b^3 + 4.

Front

What is the process for writing a polynomial in standard form?

Back

To write a polynomial in standard form, rearrange the terms so that the term with the highest degree is first, followed by the next highest, and so on.