So im starting a new unit in algebra thats all about polynomials and i has a question, can someone please simplify how to subtract polynomials, i figured out how to add them, but i find subtracting them confusing. Please help
Certainly! Subtracting polynomials involves combining like terms and applying the concept of adding the additive inverse. Here's a step-by-step explanation on how to subtract polynomials:
Step 1: Make sure all the polynomials are written in standard form. Standard form means arranging the terms in decreasing order of degree (highest exponent).
Step 2: Identify the like terms in the polynomials. Like terms have the same variables raised to the same exponents.
Step 3: Change the sign of the polynomial that you want to subtract. This can be done by changing the sign of each term within the polynomial.
Step 4: Combine the like terms. Add or subtract the coefficients of the like terms while keeping the variables and exponents the same.
Step 5: Write down the simplified polynomial after combining all the like terms.
Here's an example to illustrate the process:
Example: Subtract the polynomial (4x^2 + 3x + 2) from the polynomial (7x^2 - 2x + 5).
Step 1: Both polynomials are already in standard form.
Step 2: There are no like terms between the two polynomials since they have different variables and exponents.
Step 3: Change the sign of the polynomial being subtracted:
(7x^2 - 2x + 5) → (-7x^2 + 2x - 5)
Step 4: Combine the like terms:
(4x^2 + 3x + 2) - (7x^2 - 2x + 5)
= 4x^2 + 3x + 2 + (-7x^2) + 2x + (-5) (Note the change of sign)
Now, combine the like terms:
= (4x^2 - 7x^2) + (3x + 2x) + (2 - 5)
= -3x^2 + 5x - 3
Step 5: The simplified polynomial after combining like terms is:
-3x^2 + 5x - 3
That's it! You have successfully subtracted the polynomials. Remember to carefully combine like terms and double-check your signs when subtracting polynomials.
Of course, I'd be happy to help you understand how to subtract polynomials! Subtracting polynomials involves combining like terms and following a set of steps. Here's a simplified explanation:
1. Identify the terms that you need to subtract. Let's say you have two polynomials: Polynomial A and Polynomial B.
2. Arrange the polynomials vertically, making sure to line up the like terms. Like terms are terms with the same variable raised to the same power.
3. Change the signs of all the terms in Polynomial B. For example, if you have "3x + 4" in Polynomial B, it becomes "-3x - 4".
4. Now, you can start subtracting each term of Polynomial B from the corresponding term in Polynomial A. Combine the like terms by adding/subtracting their coefficients.
5. Write down the resulting polynomial, simplifying if possible.
Let's walk through an example to make it clearer:
Example: Subtract (4x^2 + 7x - 3) from (-3x^2 + 5x + 2).
Arrange the polynomials vertically:
-3x^2 + 5x + 2
- (4x^2 + 7x - 3)
Change the signs in Polynomial B:
-3x^2 + 5x + 2
- (-4x^2 - 7x + 3)
Now, subtract each term:
-3x^2 - (-4x^2) = -3x^2 + 4x^2 = x^2
5x - (-7x) = 5x + 7x = 12x
2 - 3 = -1
Combining all the terms, the result is:
x^2 + 12x - 1
Remember to always double-check your calculations and simplify the result if possible.
I hope this explanation helps! If you have any further questions or need additional clarification, feel free to ask.
Look at some of the videos that Sal has on polynomials
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:multiply-monomial-polynomial/v/polynomials-intro