If p(x) = x ^3 − 3x^ 2 + 2x + 5 and p(a) = p(b) = p(c) = 0, then the value of (2 − a)(2 − b)(2 − c) is

 5

Step-by-step explanation:

p(x) = x³ - 3x² + 2x + 5       p(a) = p(b) = p(c) = 0

 0  =  x³ - 3x² + 2x + 5

 0 = (x - a)(x - b)(x - c)

    = x³ − (a + b + c)x² + (ab + bc + ca)x - abc

                   ↓                          ↓                ↓

                  -3                         2                 5

-(a + b + c) = -3          

a + b + c  =  3

                             ab + bc + ca = 2

                                                         -(abc) = 5

                                                          abc = -5

(2 - a) (2 - b) (2 - c)

= 8 - 4(a + b + c) + 2(ab + bc + ca) - abc

= 8 - 4(3)             + 2(2)                  -(-5)

= 8 - 12 + 4 + 5

= 5

I think you fill the boxes with (negative infinity, positive infinity) as the domain and (negative infinity, 18]. Remember to include the correct brackets in the boxes.

Step-by-step explanation:

I had this same question so I gotchu ;). hope this helped a little bit :))!