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

To find the sum of the two expressions, we'll add them term by term. The given expressions are:

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

Let's add them step by step:

### Step 1: Combine the \(x^2\) terms
\[
6x^2 + 8x^2 = 14x^2
\]

### Step 2: Combine the \(x\) terms
\[
-36x - 5x = -41x
\]

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

### Final Sum
\[
14x^2 - 41x - 4
\]

So, the sum of the two expressions is \( \boxed{14x^2 - 41x - 4} \).

Would you like more details or have any questions?

Here are five related questions to explore further:

1. How would you find the roots of \( 14x^2 - 41x - 4 \)?
2. Can you factorize \( 14x^2 - 41x - 4 \) completely?
3. How would the solution change if the coefficient of \(x^2\) in the second expression was negative?
4. What is the value of the expression when \(x = 2\)?
5. How can we graph the expression \( 14x^2 - 41x - 4 \)?

**Tip:** Always double-check the signs when combining like terms in polynomial expressions to avoid mistakes.

Learn how to find the sum of two polynomial expressions: 6x^2 - 36x - 3 and 8x^2 - 5x - 1. Step-by-step solution provided with detailed explanation of combining like terms. Suitable for high school students studying algebra.

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