Use the grouping method to factor x^3+x^2+3x+3

(x^2+3)(x+1)

Step-by-step explanation:

Split the expression in two parts

1. x^3+x^2

2. 3x+3

Let's factor the first group. x^2(x+1)

Let's factor the second group. 3(x+1)

Combine two groups: (x^2+3)(x+1)

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: