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SAT Mathematics QUESTION #5476
Question 1
The expression $4x^2 + bx - 45$, where $b$ is a constant, can be rewritten as $(hx + k)(x + j)$, where $h, k, j$ are integers. Which of the following must be an integer?
  • $\frac{b}{h}$
  • $\frac{b}{k}$
  • $\frac{45}{h}$
  • $\frac{45}{k}$✔️
Correct Answer Explanation
Expanding $(hx+k)(x+j) = hx^2 + (hj+k)x + kj$. Thus $h=4$ and $kj=-45$. Since $k, j$ are integers, $k$ is a factor of $45$, so $\frac{45}{k}$ is an integer.