Final answer:
The quadratic expression 15x² + 11x + 2 is factored by the grouping method into (5x + 1)(3x + 2), which is verified by expansion.
Step-by-step explanation:
To factor the quadratic expression 15x² + 11x + 2 by the grouping method, we first look for two numbers that multiply to give us the product of the coefficient of the x² term (which is 15) and the constant term (which is 2), and at the same time add up to the coefficient of the x term (which is 11). These two numbers are 10 and 3. We can then rewrite the equation as 15x² + 10x + x + 2.
Next, we group the terms into two pairs and factor out any common factors: (15x² + 10x) and (x + 2). This gives us 5x(3x + 2) and (x + 2), respectively. Now, we can factor out the common factor (3x + 2), which gives us the final factored form: (5x + 1)(3x + 2).
It is always a good practice to check our answer by expanding the factored form and seeing if it matches the original expression.