Which polynomial function has a leading coefficient of –3 and roots –2, mc007-1.jpg, and 4, all with multiplicity 1?

Answer 1

For the roots of -2 and 4, the factors would be:

(x+2)(x-4)

Since they are each multiplicity of 1, what we have is correct. There is one factor for each. To tackle the leading coefficient we need to add on the -3 as a factor.

-3(x+2)(x-4)

Next we have to multiply all this out for the final polynomial. Start with FOIL, then distribute the -3.

-3(x²-2x-8) = -3x²+2x+12