What is the value of the leading coefficient a if the polynomial function p(x) = a(x + b)2(x − c) has multiplicity of 2 at the point (−1, 0) and also passes through the points (4, 0) and (0, −12)? (4 points) a) 2 b) −3 c) 3 d) −12

The given polynomial function is:



It is given that the P(x) has a zero at (-1,0) with multiplicity 2 and another zero at (4,0). So, b=1 and c=4 for the above equation. Substituting the values in equation of P(x), we get:



P(x) passes through the point (0,-12). Thus P(0) must be 12. Setting P(0) equal to 12, we get:



The polynomial thus becomes:



Therefore, leading coefficient, a , of the polynomial is -3. B option is the correct answer. 

Ibelieve the answer is b. y=0 would make the line horizontal across the x.