Create in standard form the equation of the cubic defined. Roots: -2 with multiplicity two, and 4 with multiplicity one. Point: (-3, -7)

Answer 1

Create in standard form the equation of the cubic defined. Roots: -2 with multiplicity two, and 4 with multiplicity one. Point: (-3, -7)

Multiplicity means how many of the factors there are. A root is the x value of the factor that equals zero;

Root -2 is (x+2)= 0 so there are two of that factor: (x+2)(x+2)

Root = 4 means (x-4) = 0 So the equation of factors is (x+2)(x+2)(x-4) = 0; the perfect square follows the rule ax^2 +2ab + b^2

(x^2+4x+4)(x-4) =0 multiply through to get the standard form of the equation: x^3 -12x - 16 = 0 Substitute in x = -3 to check that the y value is -7.

Answer 2

:P(x) = a(x + 2)²(x - 4)

-7 = a(-3 + 2)²(-3 - 4)

Can you solve for a and answer?