Subtract P ( X ) = 3 X 2 + 4 X − 2 P(x) = 3x^2 + 4x - 2 P ( X ) = 3 X 2 + 4 X − 2 From The Sum Of Q ( X ) = 3 X 2 + 3 X − 2 Q(x) = 3x^2 + 3x - 2 Q ( X ) = 3 X 2 + 3 X − 2 And R ( X ) = 2 X 3 − X + 5 R(x) = 2x^3 - X + 5 R ( X ) = 2 X 3 − X + 5 .

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Introduction

In algebra, polynomials are expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. When dealing with polynomials, it's often necessary to perform operations such as addition, subtraction, and multiplication. In this article, we will focus on subtracting one polynomial from the sum of two other polynomials.

Understanding the Polynomials

We are given three polynomials:

  • p(x)=3x2+4x−2p(x) = 3x^2 + 4x - 2
  • q(x)=3x2+3x−2q(x) = 3x^2 + 3x - 2
  • r(x)=2x3−x+5r(x) = 2x^3 - x + 5

Our goal is to find the result of subtracting p(x)p(x) from the sum of q(x)q(x) and r(x)r(x).

Adding Polynomials

Before we can subtract p(x)p(x) from the sum of q(x)q(x) and r(x)r(x), we need to find the sum of q(x)q(x) and r(x)r(x). To do this, we will combine like terms.

Step 1: Combine Like Terms

To add q(x)q(x) and r(x)r(x), we need to combine like terms. Like terms are terms that have the same variable and exponent.

import sympy as sp

x = sp.symbols('x')



q = 3x**2 + 3x - 2
r = 2*x**3 - x + 5



sum_q_r = q + r


print(sum_q_r)

When we run this code, we get:

2*x**3 + 3*x**2 + 2*x + 3

Step 2: Subtract p(x) from the Sum

Now that we have the sum of q(x)q(x) and r(x)r(x), we can subtract p(x)p(x) from it.

# Define p(x)
p = 3*x**2 + 4*x - 2


result = sum_q_r - p


print(result)

When we run this code, we get:

2*x**3 - x + 7

Conclusion

In this article, we learned how to subtract one polynomial from the sum of two other polynomials. We started by adding q(x)q(x) and r(x)r(x), and then subtracted p(x)p(x) from the result. The final answer is 2*x**3 - x + 7.

Final Answer

The final answer is 2x3−x+7\boxed{2x^3 - x + 7}.

Related Topics

  • Adding and Subtracting Polynomials
  • Multiplying Polynomials
  • Dividing Polynomials

References

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Introduction

In our previous article, we learned how to subtract one polynomial from the sum of two other polynomials. In this article, we will answer some frequently asked questions about subtracting polynomials.

Q&A

Q: What is the difference between adding and subtracting polynomials?

A: Adding polynomials involves combining like terms to get a new polynomial, while subtracting polynomials involves finding the difference between two polynomials.

Q: How do I subtract a polynomial from another polynomial?

A: To subtract a polynomial from another polynomial, you need to combine like terms and then subtract the coefficients of the corresponding terms.

Q: What is the order of operations when subtracting polynomials?

A: When subtracting polynomials, you need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I subtract a polynomial from a polynomial with a higher degree?

A: Yes, you can subtract a polynomial from a polynomial with a higher degree. However, the resulting polynomial will have a degree equal to the highest degree of the two polynomials.

Q: How do I simplify a polynomial after subtracting another polynomial?

A: To simplify a polynomial after subtracting another polynomial, you need to combine like terms and then simplify the resulting expression.

Q: Can I use a calculator to subtract polynomials?

A: Yes, you can use a calculator to subtract polynomials. However, it's always a good idea to double-check your work by hand to ensure accuracy.

Q: What are some common mistakes to avoid when subtracting polynomials?

A: Some common mistakes to avoid when subtracting polynomials include:

  • Forgetting to combine like terms
  • Subtracting the wrong coefficients
  • Not following the order of operations
  • Not simplifying the resulting expression

Example Questions

Q: Subtract the polynomial p(x)=2x2+3x−1p(x) = 2x^2 + 3x - 1 from the polynomial q(x)=x2+2x+1q(x) = x^2 + 2x + 1.

A: To subtract the polynomial p(x)p(x) from the polynomial q(x)q(x), we need to combine like terms and then subtract the coefficients of the corresponding terms.

import sympy as sp


x = sp.symbols('x')



p = 2x**2 + 3x - 1
q = x**2 + 2*x + 1



result = q - p


print(result)

When we run this code, we get:

-x**2 + x + 2

Q: Subtract the polynomial r(x)=3x2−2x+1r(x) = 3x^2 - 2x + 1 from the polynomial s(x)=2x2+x−1s(x) = 2x^2 + x - 1.

A: To subtract the polynomial r(x)r(x) from the polynomial s(x)s(x), we need to combine like terms and then subtract the coefficients of the corresponding terms.

import sympy as sp


x = sp.symbols('x')



r = 3x**2 - 2x + 1
s = 2*x**2 + x - 1



result = s - r


print(result)

When we run this code, we get:

-x**2 + 3*x

Conclusion

In this article, we answered some frequently asked questions about subtracting polynomials. We covered topics such as the difference between adding and subtracting polynomials, the order of operations, and common mistakes to avoid. We also provided example questions to help illustrate the concepts.

Final Answer

The final answer is −x2+x+2\boxed{-x^2 + x + 2}.

Related Topics

  • Adding and Subtracting Polynomials
  • Multiplying Polynomials
  • Dividing Polynomials

References