Question

which of the binomials below is a factor of this trinomial? x^2 + 5x - 36 A. x - 5 B. x - 9 C. x + 9 D. x^2 + 5

Answer 1

Answer:  C. x+9

===============================================

Explanation:

Think of two numbers that multiply to -36 and also add to 5. Put another way: think of two factors of -36 that add to 5.

Those two numbers are 9 and -4 since

9 times -4 = -36

9 plus -4 = 5

So we have x^2 + 5x - 36 factor into (x+9)(x-4)

x+9 is one factor

x-4 is the other factor

-------

Alternatively, you can use a graphing tool to locate the x intercepts, and that will in turn lead to the factorization. Or you could use the quadratic formula to get the job done. Completing the square is yet another tool to use. So there are multiple approaches.