Find the sum of 6, x, squared, minus, 36x
2
−3 and 8, x, squared, minus, 5, x, minus, 18x
2
−5x−1.

Let's break down the given expression step by step:

We need to find the sum of the following two expressions:

1. \(6x^2 - 36x - 3\)
2. \(8x^2 - 5x - 1\)

### Step 1: Add the coefficients of \(x^2\)
\[
6x^2 + 8x^2 = 14x^2
\]

### Step 2: Add the coefficients of \(x\)
\[
-36x - 5x = -41x
\]

### Step 3: Add the constant terms
\[
-3 - 1 = -4
\]

### Final Expression
Combining all the terms, the sum is:
\[
14x^2 - 41x - 4
\]

This is the simplified expression for the sum.

Would you like more details on any part of this process, or do you have any questions?

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Here are five related questions you might consider:

1. How do you find the difference between two polynomials?
2. What is the process for factoring a quadratic expression like \(14x^2 - 41x - 4\)?
3. How do you solve the equation \(14x^2 - 41x - 4 = 0\)?
4. What is the role of coefficients in polynomial expressions?
5. How can you check your work when adding polynomials?

**Tip:** Always align like terms (terms with the same degree of \(x\)) when adding or subtracting polynomials to avoid mistakes.

Learn how to find the sum of 6x^2 - 36x - 3 and 8x^2 - 5x - 1 with a step-by-step solution. This problem involves adding polynomials, including terms with coefficients and constant terms. Suitable for students in Grades 9-12 studying algebra and polynomials.

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