If f(x) = 3x + 5 and g(x) = –2x2 – 5x + 3, find (f + g)(x).

a. (f + g)(x) = –2x + 8

b. (f + g)(x) = –4x + 8

c. (f + g)(x) = –2x2 – 2x + 8

d. (f + g)(x) = –2x2 + 8x + 8

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.