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Factor the expression: x^2 + 7x + 10.

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Question: Factor the expression: x^2 + 7x + 10.

Options:

  1. (x + 2)(x + 5)
  2. (x - 2)(x - 5)
  3. (x + 1)(x + 10)
  4. (x - 1)(x - 10)

Correct Answer: (x + 2)(x + 5)

Solution: 

To factor x^2 + 7x + 10, we need two numbers that multiply to 10 and add to 7. The numbers 2 and 5 work. Thus, the factorization is (x + 2)(x + 5).

Factor the expression: x^2 + 7x + 10.

Practice Questions

Q1
Factor the expression: x^2 + 7x + 10.
  1. (x + 2)(x + 5)
  2. (x - 2)(x - 5)
  3. (x + 1)(x + 10)
  4. (x - 1)(x - 10)

Questions & Step-by-Step Solutions

Factor the expression: x^2 + 7x + 10.
  • Step 1: Identify the expression you want to factor, which is x^2 + 7x + 10.
  • Step 2: Look for two numbers that multiply to the constant term (10) and add up to the coefficient of the x term (7).
  • Step 3: List the pairs of numbers that multiply to 10: (1, 10) and (2, 5).
  • Step 4: Check which pair adds up to 7. The pair (2, 5) works because 2 + 5 = 7.
  • Step 5: Write the factored form using the numbers you found: (x + 2)(x + 5).
  • Factoring Quadratic Expressions – The process of rewriting a quadratic expression in the form of a product of two binomials.
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