Question

For the function f(x) = -x^3 + 2x^2 + x - 2

a. Show that (x - 1) is a factor of f(x).

b. Find other factors.

c. Sketch the graph of f(x) = -x^3 + 2x^2 x - 2

Answer 1

Explanation:

a)

`f(1)=-1^3+2*1^2+1-2=-1+2+1-2=0\\\\`

b)

Rationnel roots are divisor of -2: -1,1,-2,2

`f(-1)=-(-1)^3+2*(-1)^2+(-1)-2=1+2-1-2=0\\\\\begin{array}cccc&x^3&x^2&x&1\\---&---&---&---&---\\&-1&2&1&-2\\x=1&&-1&1&2\\&-1&1&2&0\\\\x=-1&&1&-2\\&-1&2&0\\---&---&---&---&---\\\end {array}\\\\\\f(x)=-x^3+2x^2+x-2=(x-1)(x+1)(-x+2)\\\\`

c) see picture