Math Problem Statement

Add (4x^2 - 7x + 5) and (5x^2 + 4x + 1).

Solution

The question is asking to add the polynomials:

(4x27x+5)and(5x2+4x+1).(4x^2 - 7x + 5) \quad \text{and} \quad (5x^2 + 4x + 1).

Step-by-step solution:

  1. Group like terms:

    • Combine the x2x^2-terms: 4x2+5x24x^2 + 5x^2.
    • Combine the xx-terms: 7x+4x-7x + 4x.
    • Combine the constants: 5+15 + 1.
  2. Add the terms:

    • 4x2+5x2=9x24x^2 + 5x^2 = 9x^2,
    • 7x+4x=3x-7x + 4x = -3x,
    • 5+1=65 + 1 = 6.
  3. Write the final polynomial: 9x23x+6.9x^2 - 3x + 6.

The answer provided in the screenshot, 9x23x+69x^2 - 3x + 6, is correct.


Would you like further explanation or have any specific questions?

Related Questions:

  1. What is the difference between adding and subtracting polynomials?
  2. How do you verify your answer when adding polynomials?
  3. How are like terms identified in polynomial expressions?
  4. Can you explain how to multiply two polynomials instead of adding them?
  5. How would the result change if one polynomial were subtracted instead of added?

Tip:

Always align like terms vertically when adding or subtracting polynomials to reduce errors.

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Math Problem Analysis

Mathematical Concepts

Polynomials
Addition of Polynomials
Like Terms

Formulas

Combine like terms: ax^2 + bx + c

Theorems

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Suitable Grade Level

Grade 7-9