Final answer:
To factor the trinomial x² - x - 42, we need to find two binomials whose product is equal to the trinomial. The factored form is (x - 7)(x + 6).
Step-by-step explanation:
To factor the trinomial x² - x - 42, we need to find two binomials whose product is equal to the trinomial. The binomials will have the form (x + a) and (x + b), where a and b are the constants we need to find. We need to find a and b such that when we multiply the binomials, we get x² -x - 42.
To find a and b, we can use the method of decomposition, where we factor the constant term (in this case, -42) into two numbers whose sum is equal to the coefficient of the linear term (in this case, -1). The two numbers that satisfy this condition are -7 and 6 since -7 + 6 = -1 and -7 * 6 = -42.
Therefore, the factored form is (x - 7)(x + 6).