Which of the following could be the graph of the polynomial?(x - 1)2(x + 2)?1

To determine the graph of the polynomial (x - 1)²(x + 2), we need to understand the behavior of the polynomial.

1. Identify the roots of the polynomial: The roots of the polynomial are the values of x that make the polynomial equal to zero. In this case, the roots are x = 1 (with multiplicity 2, because (x - 1) is squared) and x = -2.

2. Determine the end behavior: As x approaches positive infinity, the value of the polynomial will approach positive infinity because the leading term is positive and has an odd degree (3). As x approaches negative infinity, the value of the polynomial will approach negative infinity.

3. Identify turning points: The graph will turn at x = 1 because the root has multiplicity 2, which is even. The graph will pass straight through x = -2 because the root has multiplicity 1, which is odd.

4. Sketch the graph: Start by plotting the roots on the x-axis. As x approaches positive infinity, the graph should go up. It should pass straight through x = -2, turn around at x = 1, and then go back up as x approaches positive infinity.

Without a specific set of graphs to choose from, this is the general shape and behavior you should look for in the graph of the polynomial (x - 1)²(x + 2).