Use the Rational Root theorem to determine the factors of x^3 - 2x^2 - 13x - 10 given that one factor is (x + 1)

The correct option is;

D. (x - 5)·(x + 2)·(x + 1)

Step-by-step explanation:

The Rational Root theorem is expressed mathematically as follows;

The given polynomial is presented as follows;

x³ - 2·x² - 13·x - 10

A factor of the polynomial = (x + 1)

The factors of the constant term, -10 = -10, -5, -2, -1, 10, 5, 2, and 1

The factors of the leading coefficient, (the coefficient of the variable having the highest degree or power, x³) = 1

Given that (x + 1) is a known factor, the other two factors are either (x + 5) and (x - 2) or (x - 5) and (x + 2)

The option, that combines (x + 1) and the other two factor combination is (x - 5)·(x + 2)·(x + 1)

∴ The solution which meets the condition is (x - 5)·(x + 2)·(x + 1)

We check;

(x - 5)·(x + 2)·(x + 1)  = x³ - 2·x² - 13·x - 10

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

answer: 1+1

step-by-step explanation: 1+1 is at least 2