Math Problem Statement

Given that f(x) = x^2 - 11x + 18 and g(x) = x - 2, find f(x) + g(x) and express the result as a polynomial in simplest form.

Solution

We are given two functions:
f(x)=x211x+18f(x) = x^2 - 11x + 18 and g(x)=x2g(x) = x - 2.

We are tasked with finding f(x)+g(x)f(x) + g(x) and expressing the result as a polynomial in its simplest form.

Step-by-step solution:

  1. Start by writing the expression for f(x)+g(x)f(x) + g(x): f(x)+g(x)=(x211x+18)+(x2)f(x) + g(x) = (x^2 - 11x + 18) + (x - 2)

  2. Now, combine like terms: =x211x+x+182= x^2 - 11x + x + 18 - 2 =x210x+16= x^2 - 10x + 16

Thus, the simplified polynomial is: f(x)+g(x)=x210x+16f(x) + g(x) = x^2 - 10x + 16

Would you like more details or further clarification?

Here are five related questions to expand your understanding:

  1. What is the difference between combining like terms and multiplying polynomials?
  2. How would you subtract g(x)g(x) from f(x)f(x) instead of adding them?
  3. Can you factor the resulting polynomial x210x+16x^2 - 10x + 16?
  4. What happens when you multiply f(x)f(x) and g(x)g(x) instead of adding them?
  5. How does changing the value of the constants in f(x)f(x) and g(x)g(x) affect their sum?

Tip: When simplifying polynomials, always make sure to group and combine like terms, which are terms with the same variable raised to the same power.

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Math Problem Analysis

Mathematical Concepts

Polynomial Addition
Algebra
Combining Like Terms

Formulas

f(x) + g(x) = (f(x) + g(x))

Theorems

None

Suitable Grade Level

Grades 8-10