why is x-5 a factor of x2(sqd)-x-20?

Question

This question was on a sample placement test, and I don't understand how they came to the answer. The question is:
Which of the following is a factor of the polynomial x2-x-20?

The '2' is actually indicating that the first x is squared, but I don't know how to shrink the 2 :(

The correct answer is x-5

Where did the 5 come from? I don't get it at all...

TomV · Accepted Answer

The polynomial is x²-x-20
Factor the polynomial:
x² - x - 20 = (x-5)(x+4)
The two factors of the polynomial are (x-5) and (x+4) because if you multiply (x-5) times (x+4), you get:
(x-5)(x+4) = x(x+4) - 5(x+4) = x² + 4x - 5x - 20 = x² - x - 20
which is the original polynomial.

MechEng2030 · Answer

You have to factor the expression. That is, you must see what two numbers multiply to -20 and add up to -1. Those two numbers are -5 and 4.

x^2 - x - 20 = (x - 5)(x + 4)

? · Answer

x^2 - x - 20 equals (x - 5 ) ( x + 4)

The -5 and +4 multiply to give -20
They add to give -1, for the -x part.  Notice that -x = -1x,

why is x-5 a factor of x2(sqd)-x-20?

3 Answers