Penjumlahan dan Pengurangan Polinomial Suku Banyak | Matematika SMA

Introduction

This tutorial provides a comprehensive guide on how to perform addition and subtraction of polynomials, a fundamental concept in algebra typically introduced in the 11th grade. Understanding these operations is essential for solving more complex mathematical problems.

Step 1: Understanding Polynomials

• A polynomial is an expression made up of variables and coefficients.
• The general form of a polynomial is:
  ( P(x) = 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 (coefficients), and ( n ) is a non-negative integer (degree of the polynomial).

Tips for Identifying Polynomials

• Check if the expression contains negative exponents or variables in the denominator; these disqualify it from being a polynomial.

Step 2: Adding Polynomials

To add polynomials, follow these steps:

1. Align Like Terms: Group the terms that have the same degree (power of x).
2. Combine Coefficients: Add the coefficients of the like terms together.
3. Write the Result: Rewrite the polynomial with the combined terms.

Example

Given the polynomials:
( P(x) = 3x^2 + 2x + 1 )
( Q(x) = 5x^2 + 3x + 4 )

• Align:
  • ( (3x^2 + 5x^2) + (2x + 3x) + (1 + 4) )
• Combine:
  • ( 8x^2 + 5x + 5 )
• Result:
  • ( P(x) + Q(x) = 8x^2 + 5x + 5 )

Step 3: Subtracting Polynomials

Subtracting polynomials is similar to addition but involves changing the sign of the polynomial being subtracted. Follow these steps:

1. Distribute the Negative Sign: Change the sign of each term in the second polynomial.
2. Align Like Terms: Group the terms with the same degree.
3. Combine Coefficients: Subtract the coefficients of like terms.
4. Write the Result: Rewrite the polynomial with the resulting terms.

Example

Given the polynomials:
( P(x) = 3x^2 + 2x + 1 )
( Q(x) = 5x^2 + 3x + 4 )

• Change the sign of ( Q(x) ):
  • ( -Q(x) = -5x^2 - 3x - 4 )
• Align:
  • ( (3x^2 - 5x^2) + (2x - 3x) + (1 - 4) )
• Combine:
  • ( -2x^2 - x - 3 )
• Result:
  • ( P(x) - Q(x) = -2x^2 - x - 3 )

Conclusion

Understanding how to add and subtract polynomials is crucial for mastering algebra. Practice these steps with various polynomial expressions to improve your skills. As you progress, you can explore further operations such as multiplication and division of polynomials to enhance your mathematical knowledge.