Is (x − 2) a factor of f(x) = x^3 − 2x^2 + 2x + 3? Use either the remainder theorem or the factor theorem to explain your reasoning.

isn't a factor of .

Step-by-step explanation:

By the factor theorem, for any constant , is a factor of polynomial if and only if . Note that means that substituting all in with and evaluating gives .

For example, the polynomial in this question is . The question is asking whether is a factor of .

By the factor theorem with , would indeed be a factor of if and only if . To find the value , simplify replace all "" in the definition of with :

.

In other words, . By the contrapositive of factor theorem, would not be a factor of .

answer: rolling a number cube and flipping a coin.

step-by-step explanation:

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9