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Factor the polynomial x^2 + 7x + 10.

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

Options:

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

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

Solution: 

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

Factor the polynomial x^2 + 7x + 10.

Practice Questions

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

Questions & Step-by-Step Solutions

Factor the polynomial x^2 + 7x + 10.
  • Step 1: Identify the polynomial 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 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 factors using the two numbers you found. This gives you (x + 5)(x + 2).
  • Factoring Quadratic Polynomials – This involves rewriting a quadratic expression in the form ax^2 + bx + c as a product of two binomials.
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