What is the sum of the given polynomials in standard form?

(*x*2 – 3*x*) + (–2*x*2 + 5*x* – 3)

–3*x*2 + 8*x* – 3

–*x*2 – 2*x* – 3 

3*x*2 – 8*x* + 3 

–*x*2 + 2*x* – 3

To find the sum of the given polynomials, let's first rewrite each polynomial clearly and then add them together term by term.

Given polynomials:

1. \( x^2 - 3x \)
2. \( -2x^2 + 5x - 3 \)
3. \( -3x^2 + 8x - 3 \)
4. \( -x^2 - 2x - 3 \)
5. \( 3x^2 - 8x + 3 \)
6. \( -x^2 + 2x - 3 \)

We will now add the corresponding coefficients of each term together.

### Combining Like Terms

**\( x^2 \) terms:**
\[ 1x^2 + (-2x^2) + (-3x^2) + (-x^2) + 3x^2 + (-x^2) = 1 - 2 - 3 - 1 + 3 - 1 = -3x^2 \]

**\( x \) terms:**
\[ -3x + 5x + 8x - 2x - 8x + 2x = -3 + 5 + 8 - 2 - 8 + 2 = 2x \]

**Constant terms:**
\[ 0 + (-3) + (-3) + (-3) + 3 + (-3) = -3 - 3 - 3 + 3 - 3 = -9 \]

### Summing Up

The sum of the given polynomials in standard form is:
\[ -3x^2 + 2x - 9 \]

Would you like any more details or have any questions about this solution?

Here are 5 numbered questions you can ask:

1. How do you simplify the sum of polynomials step-by-step?
2. Can you explain the process of combining like terms in polynomials?
3. What are the key differences between polynomials and other algebraic expressions?
4. How do you factor the resulting polynomial from this sum?
5. What are the applications of polynomial addition in real-life scenarios?

**Tip:** When adding or subtracting polynomials, always align like terms (terms with the same power of \(x\)) to simplify the process.

Explore how to find the sum of given polynomials in standard form with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomials, combining like terms, and standard form representation. Suitable for students in Grades 7-9.

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