Subtracting Polynomials 4-4

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 subtracting the corresponding terms of another polynomial, combining like terms in the process.

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, 3x and 5x are like terms, while 3x and 3x^2 are not.

Front

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

Back

The result is (5x^2 - 2x + 4) - (2x^2 + 3x - 5) = 3x^2 - 5x + 9.

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 - x, the degree is 3.

Front

What is the coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 3x^2, 3 is the coefficient.

Front

How do you combine like terms when subtracting polynomials?

Back

To combine like terms, group the terms with the same variable and exponent, and then perform the arithmetic operation (addition or subtraction) on their coefficients.

Front

What is the polynomial subtraction rule?

Back

The polynomial subtraction rule states that to subtract one polynomial from another, you can add the opposite of the polynomial being subtracted.

Front

What is the simplified form of the expression: (4p + 5) - (2p - 3)?

Back

The simplified form is 2p + 8.

Front

What is the importance of parentheses in polynomial subtraction?

Back

Parentheses indicate the order of operations and help clarify which terms are being subtracted, especially when negative signs are involved.