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Kristin Fracchia

ACT Challenge Question 12: What is S? – Explanation

Magoosh ACT Challenge Question

Math whizzes! Below you’ll find the answer and explanation to our ACT Math Challenge Question of the Week. But if you missed our earlier post, take a stab at the following question before you peek below:

ACT Challenge Question 12

What would s have to be so that {x^3} + {5x^2} + sx + 6 is divisible by (x + 2)?

  1. 9
  2. 5
  3. 2
  4. -6
  5. -13


Answer and Explanation

A: 9

Probably the most elegant way to solve this problem is to remember the Factor Theorem. This is a useful trick for problems like this on the ACT. The Factor Theorem states that a polynomial P(x) is divisible by binomial (x – c) if and only if P(c) = 0.  In order for a polynomial to be divisible by a linear binomial, the polynomial and the binomial must have the same root.

If we want polynomial P(x) to be divisible by (x + 2), it must be true that P(– 2) = 0.  In other words, x = -2 must be a root of the equation.


So our answer is A.


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About Kristin Fracchia

Kristin makes sure Magoosh's sites are full of awesome, free resources that can be found by students prepping for standardized tests. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004 and has helped students prepare for standardized tests, as well as college and graduate school admissions, since 2007. She enjoys the agony and bliss of train running, backpacking, hot yoga, and esoteric knowledge.

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