Is (x − 2) a factor of f(x) = x3 − 2x2 + 2x + 3? use either the remainder theorem or the factor theorem to explain your reasoning.

x-2 is not a factor of x^3 - 2x^2+2x+3

Step-by-step explanation:

Given

In order to check we have to put

x-2 = 0

x=2

We will put x=2 in given expression. If the expression becomes equal to zero that means 2 is a factor of this expression. If the answer is not zero, 2 is not a factor of the given expression.

So putting 2,

As the answer is not equal to zero, x-2 is not a factor of given expression ..

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation: