Use complete sentences to explain how to use linear factors to determine the equation of a polynomial function.

Answer 1

If you can factor any polynomial function into linear factors, each factor can be set equal to zero, and solved for one of the solutions to the polynomial function.

x^2 -3x -10 = 0

can be factored into 2 linear factors

(x-5)(x+2) = 0

if either factor = 0 then the polynomial = 0

x-5= 0 means x =5

x+2=0 means x=-2

That can be generalized to any degree polynomial

if ax^n+bx^n-1 + .... f = 0

can be factored into

(x-g)(x-h)(x-j)...(x-m) = 0

then solutions to the polynomial are

g, h, j, ....m

It's similar to

if abc = 0

then a=0, b=0 and c=0 are solutions,

since if either a, b or c = 0 then abc=0