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

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

Options:

  1. (x + 5)(x + 2)
  2. (x - 5)(x - 2)
  3. (x + 10)(x - 1)
  4. (x - 7)(x - 10)

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

Solution: 

We need two numbers that multiply to 10 and add to 7. The numbers 5 and 2 work. Thus, the factored form is (x + 5)(x + 2).

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

Practice Questions

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

Questions & Step-by-Step Solutions

Factor the quadratic expression x^2 + 7x + 10.
  • Step 1: Identify the quadratic expression, which is x^2 + 7x + 10.
  • Step 2: Look for two numbers that multiply to the constant term (10) and add to the coefficient of the x term (7).
  • Step 3: The two numbers that work are 5 and 2 because 5 * 2 = 10 and 5 + 2 = 7.
  • Step 4: Write the factored form using these two numbers: (x + 5)(x + 2).
  • Factoring Quadratics – The process of rewriting a quadratic expression in the form of a product of two binomials.
  • Finding Roots – Identifying two numbers that multiply to the constant term and add to the linear coefficient.
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