John gave the following explanation for factoring the trinomial x2 - x - 2: "I need to find factors of -2. -1 and 2 multiply to -2 so my factors are (x - 1)(x + 2)."

Question

anonymous · Answer

Part 1: Are John's factors correct? If not, explain where he made his mistake.

Part 2: What could John have done to check the accuracy of his factors before submitting his Module 3 test?

anonymous · Answer

@amistre64 could you help me with this one too?

marissalovescats · Answer

Johns factors are not correct. His two binomials of (x-1)(x+2) would come out to make: 

x times x = x^2
2x-1x=x
-1 times 2 is -2

x^2+x-2 is not x^2-x-2. 

So what do you think we can do to fix that?

mathstudent55 · Answer

Part 1. His factors are incorrect. To factor that polynomial you do need two factors of -2, but they need to add to -1. In this case, the two factors he chose, -1 and 2 do not add to -1, so they are not the correct factors.

marissalovescats · Answer

To check your factors to ensure they are correct, you do what I just did. You FOIL your two binomials to see if it comes out to the trinomial you started with.

mathstudent55 · Answer

Part 2. He could have multiplied out his factored form to see if he ends up with the original polynomial. If he doesn't, then he knows the factoring is wrong.