Final Answer:
The correct factor of x^2 − 21x + 110 is (x - 10), so the answer is option B) x − 10.
Step-by-step explanation:
The given quadratic expression is x^2 − 21x + 110. To find the factors, we need to look for two numbers that multiply to the constant term (110) and add up to the coefficient of the linear term (-21). In this case, those two numbers are -10 and -11. Therefore, the factored form of the quadratic expression is (x - 10)(x - 11). So, the correct factor among the given options is (x - 10).
In more detail, we can use the factoring method or the quadratic formula to find the factors. Factoring involves breaking down the quadratic expression into its two linear factors. In this case, it can be factored as (x - 10)(x - 11). The quadratic formula, x = [-b ± √(b^2 - 4ac)] / (2a), can also be applied to find the roots of the quadratic equation, and from there, the factors can be determined. However, in this instance, factoring is a more straightforward method.
In conclusion, the correct factor of x^2 − 21x + 110 is (x - 10), which corresponds to option B) x − 10.