Factor the expression: x^2 + 3x - 10

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Question: Factor the expression: x^2 + 3x - 10

Options:

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

Solution:

We need two numbers that multiply to -10 and add to 3. The numbers 5 and -2 work. Thus, the factorization is (x + 5)(x - 2).

Factor the expression: x^2 + 3x - 10

Factor the expression: x^2 + 3x - 10

Step 1: Identify the expression you want to factor, which is x^2 + 3x - 10.
Step 2: Look for two numbers that multiply to -10 (the constant term) and add to 3 (the coefficient of x).
Step 3: The two numbers that work are 5 and -2 because 5 * -2 = -10 and 5 + (-2) = 3.
Step 4: Rewrite the expression using these two numbers: x^2 + 5x - 2x - 10.
Step 5: Group the terms: (x^2 + 5x) + (-2x - 10).
Step 6: Factor out the common factors in each group: x(x + 5) - 2(x + 5).
Step 7: Now, you can factor out (x + 5): (x + 5)(x - 2).

Factoring Quadratic Expressions – This involves rewriting a quadratic expression in the form ax^2 + bx + c as a product of two binomials.
Finding Factors – Identifying two numbers that multiply to the constant term and add to the linear coefficient.