Question

Which polynomial could have the following graph?

Answer 1

Hi,
Roots are 2, -1,-3.So y=(x-3)(x+1)(x+3)
Answer B

Answer 2

Answer: $y=(x-2)(x+1)(x+3)$

Step-by-step explanation:

From the given graph, it can be seen that the x intercepts of the graph are

$x=-3,\ x=-1,\ x=2$

It implies the value of y at the above points must be zero.

[x-intercept is of the form (a,0), where the value of y is zero.]

It implies $x=-3,\ x=-1,\ x=2$ are the zeroes of the polynomial graphed.

It implies $(x-2),\ (x+1),\ (x+3)$ are the factors of the polynomial graphed.

[By Factor theorem]

Thus the polynomials should be :  $y=(x-2)(x+1)(x+3)$ which is the correct polynomial for the given graph.