Math Problem Statement

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

Solution

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

  1. 6x236x36x^2 - 36x - 3
  2. 8x25x18x^2 - 5x - 1

Let's add them step by step:

Step 1: Combine the x2x^2 terms

6x2+8x2=14x26x^2 + 8x^2 = 14x^2

Step 2: Combine the xx terms

36x5x=41x-36x - 5x = -41x

Step 3: Combine the constant terms

31=4-3 - 1 = -4

Final Sum

14x241x414x^2 - 41x - 4

So, the sum of the two expressions is 14x241x4\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 14x241x414x^2 - 41x - 4?
  2. Can you factorize 14x241x414x^2 - 41x - 4 completely?
  3. How would the solution change if the coefficient of x2x^2 in the second expression was negative?
  4. What is the value of the expression when x=2x = 2?
  5. How can we graph the expression 14x241x414x^2 - 41x - 4?

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

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Math Problem Analysis

Mathematical Concepts

Polynomial expressions
Combining like terms

Formulas

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Theorems

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Suitable Grade Level

High School