Math Problem Statement

x^2+9x+20 factorize

Solution

To factorize the quadratic expression x2+9x+20x^2 + 9x + 20, we will find two numbers that multiply to 20 (the constant term) and add to 9 (the coefficient of the linear term).

Steps:

  1. The quadratic expression is x2+9x+20x^2 + 9x + 20.
  2. We need to find two numbers that multiply to 20 and add up to 9.
    • The numbers are 4 and 5 because 4×5=204 \times 5 = 20 and 4+5=94 + 5 = 9.
  3. We can now write the factorized form as: (x+4)(x+5)(x + 4)(x + 5)

So, the factorized form of x2+9x+20x^2 + 9x + 20 is (x+4)(x+5)(x + 4)(x + 5).

Would you like more details or have any questions?

Here are 5 related questions for practice:

  1. Factorize x2+8x+12x^2 + 8x + 12.
  2. What is the factorized form of x27x+10x^2 - 7x + 10?
  3. Factorize x2+6x+8x^2 + 6x + 8.
  4. Find the factors of x2+10x+21x^2 + 10x + 21.
  5. What are the factors of x23x28x^2 - 3x - 28?

Tip: Always check the product of the factors to verify your result!

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Math Problem Analysis

Mathematical Concepts

Algebra
Factorization
Quadratic Expressions

Formulas

Factorization of quadratic expressions: (x + p)(x + q) where p * q = constant term and p + q = coefficient of x

Theorems

Zero Product Property
Factor Theorem

Suitable Grade Level

Grades 8-10