In this aptitude (simplification and algebra) question, expand the product (x + 9)(8 - 5x), collect like terms, and then find the coefficient of x in the resulting expression.

Introduction / Context:
This question assesses basic algebraic manipulation, specifically binomial expansion and identification of coefficients. Such tasks are common in algebra based aptitude sections and also form a foundation for more advanced topics like polynomial division and factorisation.

Given Data / Assumptions:
We are given the product (x + 9)(8 - 5x).
We must expand this product and identify the coefficient of x in the simplified expression.

Concept / Approach:
To expand the product of two binomials, we use the distributive property, sometimes remembered as the FOIL method: multiply each term in the first bracket by each term in the second bracket and then collect like terms. After simplification, the coefficient of x is simply the number multiplied by x in the resulting polynomial.

Step-by-Step Solution:
Start with (x + 9)(8 - 5x). Multiply x by each term in the second bracket: x * 8 = 8x and x * (-5x) = -5x^2. Multiply 9 by each term in the second bracket: 9 * 8 = 72 and 9 * (-5x) = -45x. Collect all terms: -5x^2 + 8x - 45x + 72. Combine the x terms: 8x - 45x = -37x. So the expanded expression is -5x^2 - 37x + 72. Therefore the coefficient of x is -37.

Verification / Alternative check:
We can check quickly by plugging in a convenient value of x and comparing partial contributions. However, the algebraic expansion is already clear and straightforward. Writing the product in standard form ax^2 + bx + c shows directly that b is the coefficient of x. From our work, b equals -37, so the answer is confirmed.

Why Other Options Are Wrong:
Option 37 corresponds to forgetting the negative sign in front of 5x in the second factor. Options -53 and 53 are unrelated to the combined x term and may come from mixing coefficients of x^2 and x. Option 8 is the coefficient of x before combining like terms, ignoring the -45x contribution. Since correct simplification gives -37x as the linear term, only -37 is accurate.

Common Pitfalls:
Students often drop negative signs when multiplying, especially with the term -5x. Another issue is failing to combine all linear terms or mixing quadratic and linear coefficients. Writing every intermediate product explicitly and then grouping like terms systematically helps reduce such errors.

Final Answer:
After expansion and simplification, the coefficient of x in (x + 9)(8 - 5x) is -37.