Final answer:
To factor the polynomial x²−x−30, find two numbers that multiply to -30 and add to -1, leading to the factored form as (x + 5)(x - 6).
Step-by-step explanation:
To factor the given polynomial: x²−x−30, we are looking for two numbers that multiply to -30 and add up to -1 (the coefficient of the x term).
Through trial and error or systematic pairing of factors of -30, we can find that the numbers are +5 and -6 since (5)(-6) = -30 and 5 + (-6) = -1.
Therefore, the factored form of the polynomial is:
(x + 5)(x - 6)
We have effectively rewritten the original quadratic as the product of two linear factors.