Question

Which point is a point where the graph of y= (x + 2)(x2 + 4x+3) crosses the x-axis?

A. (-3,0)
B. (2,0)
C. (1,0)
D. (3,0)

Answer 1

A. (-3, 0)

Explanation:

There should seemingly be 3 points where this graph crosses the x-axis. To determine each of them we can respectively set y to 0;

0 = (x+2)(x^2 + 4x + 3),

A quick way we can factor x^2 + 4x + 3 is using Vieta's Theorem. I don't ideally use it but since x1 * x2 = 3, and x1 + x2 = - 4 then x1 = -1 and x2 = -3. Since these are the roots the factored expression should be (x + 1)(x + 3).

0 = (x+ 2)(x +1)(x + 3),

x = -2, x= - 1, x= - 3

So the x-intercepts are (-2,0), (-1, 0), and (-3,0)

Your answer is option a