Final answer:
The statement about the division (x²-3x-18)÷(x-6) can be verified by factoring the quadratic equation, revealing that the result of the division simplifies to x+3.
Step-by-step explanation:
To determine the truth of the statement regarding the division (x²-3x-18)÷(x-6), we must perform polynomial division or factor the quadratic equation, if possible. Given that both multiplication or division by the same number on both sides of an equation does not change equality, we can apply these operations to simplify or solve equations. Additionally, negative exponents can invert terms to the denominator, which might be relevant in simplifying algebraic expressions.
For the division at hand, if we factored the quadratic equation x²-3x-18, we would find that it can be factored as (x-6)(x+3). Hence, when we divide by x-6, we are left with x+3, assuming x != 6, since division by zero is undefined. Thus, we can simplify the given expression to x+3 after performing the division.
Moreover, when solving a quadratic equation, we can use the quadratic formula if factoring is not available or not obvious. This is demonstrated by rearranging the equation into a standard form such as ax² + bx + c = 0 and then applying the formula.