Subtraction of polynomials

Definition

Subtraction of polynomials involves taking one polynomial and subtracting another, which is a fundamental operation in algebra. This process requires aligning like terms, ensuring that terms with the same degree are combined correctly. Understanding how to effectively subtract polynomials is crucial for manipulating algebraic expressions and simplifying complex mathematical equations.

5 Must Know Facts For Your Next Test

1. To subtract polynomials, first distribute the negative sign across the second polynomial before combining like terms.
2. The result of subtracting one polynomial from another can still be a polynomial, maintaining the structure of the expression.
3. It's essential to write polynomials in standard form (from highest degree to lowest) after performing subtraction for clarity.
4. Subtraction is essentially adding a negative polynomial, so understanding addition of polynomials is helpful when learning subtraction.
5. Errors often occur during subtraction when like terms are not properly aligned or combined, so careful organization is key.

Review Questions

• How do you approach subtracting two polynomials step by step?
  • To subtract two polynomials, start by rewriting the first polynomial as it is. Next, distribute the negative sign across all terms of the second polynomial. After that, combine like terms by adding or subtracting their coefficients. Ensure that each term is correctly aligned by degree to avoid mistakes during the combination process.
• Why is it important to understand like terms when subtracting polynomials?
  • Understanding like terms is crucial when subtracting polynomials because they are the only terms that can be combined. By identifying like terms, you ensure that you are accurately performing the subtraction operation and maintaining the integrity of the polynomial's structure. Misaligning or incorrectly combining unlike terms can lead to significant errors in your final answer.
• Evaluate the expression (3x^2 + 5x - 2) - (4x^2 - 3x + 6) and explain your steps.
  • To evaluate (3x^2 + 5x - 2) - (4x^2 - 3x + 6), start by distributing the negative sign across the second polynomial: (3x^2 + 5x - 2) - 4x^2 + 3x - 6. Now combine like terms: (3x^2 - 4x^2) + (5x + 3x) + (-2 - 6), which results in -1x^2 + 8x - 8. This example illustrates how careful subtraction and combining like terms yield a new polynomial.

Related terms

Polynomial:

An algebraic expression that consists of variables raised to non-negative integer powers, combined using addition, subtraction, or multiplication.

Like Terms:

Terms within a polynomial that have the same variable raised to the same power, allowing them to be combined through addition or subtraction.

Degree of a Polynomial: The highest power of the variable in a polynomial, which determines the polynomial's classification and behavior.