Answer:
(x + 5)(x - 4)
Step-by-step explanation:
To factor a polynomial of a 2nd degree - with the highest degree variable's coefficient being 1 - we should find two numbers, m and n, whose sum equates to the coefficient of x and whose product equates to the constant value.
In other words, if a polynomial is given by the equation x^2 + bx + c, we should find two numbers m and n such that:
m + n = b,
m * n = c.
In our case, the coefficient of x is 1 and the constant value is -20.
Two numbers that satisfy this condition are m = 5 and n = -4.
Therefore, x^2 + x - 20 can be factorized as (x + 5)(x - 4).
If we were to expand this product, we would get:
[tex](x + 5)(x - 4) = x^2 - 4x + 5x - 20 = x^2 + x - 20[/tex]
Which is exactly what we started with.
