Me! will choose brainliest (:
is the given linear expression a factor of the polynomial? show your work.
g(x)=3x^3+2x^2-17x+6; x+3

Long way: try to divide. But we are lazy, so it's no go. Option number one: all rational numbers that could give you a division can be taken from "THE List": you build it by taking the constant term, that is 6, and all its divisors (1,2,3,6), the highest term coefficent, 3 in this case, its divisors (1,3) , and you divide every one in the first list by the second, and adding a in front of them. Our list is: .

Since -3 is part of THE List, it might be a divisor - that system would garantee you that, for example, x-4 would NOT be a factor.

Cheap way. if (x+3) is a factor of g(x), then g(-3) = 0. Let's replace.

Since we didn't get zero, is not a factor of g(x)

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.