Final answer:
After setting the two given expressions equal to each other, we derive the equation 8x² - x + 155 = 0. None of the provided factored options match the derived equation, implying a possible error in the original problem or in the provided choices.
Step-by-step explanation:
The student is tasked with choosing the equivalent factored form for the quadratic expression 10x² + 150 - 9, which simplifies to 10x² + 141, to match with the expression 2x² + x - 14. To find the equivalent factored form, we first need to equal the two expressions:
10x² + 141 = 2x² + x - 14
Subtracting 2x², x, and 14 from both sides gives:
8x² - x + 155 = 0
By using the quadratic formula, √x = (-b ± √(b² - 4ac))/(2a), where a = 8, b = -1, and c = 155, we can solve for 'x'. This expression does not match any of the factored options given, so there appears to be a mistake. Normally, to factor, one would find two numbers that multiply to give ac (1240 in this case) and add to give b (-1). However, no such real numbers exist for the given expression, indicating a possible typo in the original problem or choices. Factoring typically applies to expressions that are equal to zero.
Therefore, the selections provided (a) through (d) do not accurately represent the factored form of the given quadratic equation after equating the two expressions. The student may need to reassess the original problem for any errors or seek additional options that are correct.