Final answer:
D) (4x + 5)(2x + 1). To choose the equivalent factored form for the given expression, we need to simplify both sides of the equation and factor the quadratic terms. The correct answer is D) (4x + 5)(2x + 1).
Step-by-step explanation:
To choose the equivalent factored form for the given expression, we need to simplify both sides of the equation and factor the quadratic terms.
Starting with the left side of the equation, we group the quadratic terms together: 10x² + 15² - 9 = (10x² + 15²) - 9 = (10x² + 225) - 9 = 10x² + 216.
Now, we simplify the right side of the equation: 2x² + 3 - 14 = 2x² - 11.
Combining the simplified expressions for both sides, we have: 10x² + 216 = 2x² - 11.
Next, we move all terms to one side of the equation to set it equal to zero: 10x² + 216 - 2x² + 11 = 0.
Finally, we can factor the quadratic expression to find the equivalent factored form. Solving the equation gives us: (4x + 5)(2x + 1) = 0.
Therefore, the correct answer is D) (4x + 5)(2x + 1).