Use the graph of the polynomial function fx a to solve fx 0

Use the graph of the polynomial function f(x) (a) to solve f(x) = 0, and (b) find the factorization of f(x). f(x)= -x^4 + 5x^3 + 3x^2 - 13x - 10 (a) Choose the correct solution foe f(x) = 0. A. x = -2 and x = - 5 B. x = 2 and x =5 C. x = 1, x = - 2, and x= - 5 D. x = -1, x = 2 and x = 5 (b) The factorization of the polynomial function f (x) is Type your answer in factored form.)

Solution

f(x) = -x^4 +5x^3+3x^2-13x -10

-x^4 +5x^3+3x^2-13x -10 = 0

the rational roots of the equation are

+- { 1 , 2 , 5 , 10 }

checking each root one by one by plugging in to the equation we get

at x = -1 , f(x) = 0

therefore , x = -1 is real zero

x = 2 , f(x) = 0

x = 2 is real zero

x = 5 is real zero

factored form is

f(x) = - (x+1)^2 (x-2) (x-5)