Subtracting Polynomials

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. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What does it mean to subtract polynomials?

Back

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

Front

How do you identify like terms in polynomials?

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 raised to the power of 2.

Front

What is the first step in subtracting polynomials?

Back

The first step in subtracting polynomials is to distribute the negative sign to each term in the polynomial being subtracted.

Front

What is the result of subtracting (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

The result is -8n^2 - 8n + 3.

Front

What is the result of subtracting (5x + x^2 - 4) - (4x - x^2 + 6)?

Back

The result is 2x^2 + x - 10.

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

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

Back

The result is -2x^3 + x^2 + 1.

Front

What is the importance of combining like terms when subtracting polynomials?

Back

Combining like terms is crucial because it simplifies the expression and allows for a clearer understanding of the polynomial's overall value.

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 the polynomial 4x^3 + 2x^2 - x + 5, the degree is 3.