Addition of Polynomials Math Worksheets | Ages 11-13 Activities - Free Printable

The image provided is an informational sheet about polynomial addition, aimed at students aged 11-13 or in 7th and 8th grades (USA). It introduces the concept of polynomials and explains how to add them. Below is a detailed explanation of the solution to the problem of adding polynomials, along with key concepts.

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Key Concepts from the Image

1. Definition of Polynomials:
- Polynomials are mathematical expressions that consist of:
- Coefficients: Numbers that multiply variables.
- Variables: Letters representing unknown values (e.g., \( x \), \( y \)).
- Constants: Fixed numbers (e.g., 5, -3).
- Exponents: Powers to which variables are raised (e.g., \( x^2 \)).
- Operations allowed in polynomials include addition, subtraction, multiplication, and division (but not division by a variable).

2. Adding Polynomials:
- To add polynomials, you combine like terms.
- Like terms are terms that have the same variables raised to the same powers. For example:
- \( 3x^2 \) and \( 5x^2 \) are like terms.
- \( 4xy \) and \( -2xy \) are like terms.
- \( 7 \) and \( -3 \) are like terms (both are constants).

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Step-by-Step Solution for Adding Polynomials

#### Example Problem:
Add the following polynomials:
\[ P(x) = 3x^2 + 2x - 5 \]
\[ Q(x) = -x^2 + 4x + 6 \]

#### Step 1: Write the polynomials side by side.
\[ P(x) + Q(x) = (3x^2 + 2x - 5) + (-x^2 + 4x + 6) \]

#### Step 2: Group like terms together.
- Terms with \( x^2 \): \( 3x^2 \) and \( -x^2 \)
- Terms with \( x \): \( 2x \) and \( 4x \)
- Constant terms: \( -5 \) and \( 6 \)

So, rewrite the expression grouping like terms:
\[ P(x) + Q(x) = (3x^2 - x^2) + (2x + 4x) + (-5 + 6) \]

#### Step 3: Add the coefficients of the like terms.
- For \( x^2 \)-terms: \( 3x^2 - x^2 = 2x^2 \)
- For \( x \)-terms: \( 2x + 4x = 6x \)
- For constant terms: \( -5 + 6 = 1 \)

#### Step 4: Write the final polynomial.
Combine all the results:
\[ P(x) + Q(x) = 2x^2 + 6x + 1 \]

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Final Answer:

\[ \boxed{2x^2 + 6x + 1} \]

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Explanation:

- The process of adding polynomials involves identifying and combining like terms. This ensures that only terms with the same variables and exponents are added together.
- By systematically grouping and simplifying, we can efficiently find the sum of any two polynomials.

This method is fundamental in algebra and helps build a strong foundation for more complex operations involving polynomials.