Question

Expand and simplify each function. Evaluate at f(- 2).

a. f(x) = (x + 1)(x - 2)(x + 3)

b. f(x) = (2x ^ 2 - 3)(x ^ 3 + 1)

Answer 1

(a) $f(x) = (x+1)(x-2)(x+3)$

$\rightarrow$ $(x^2 -2x + x -2)(x+3)$

$\rightarrow (x^2 -x -2)(x+3)$

$\rightarrow x^3 + 3x^2 - x^2 -3x -2x -6$

$\rightarrow x^3 +2x^2 -5x -6$

For f(-2), put x= -2

$f(-2) = (-2)^3 +2(-2)^2 -5(-2) -6$

$\rightarrow -8 +8 +10 -6$ = 4

So f(-2) = 4

(b) $f(x) = (2x^2 -3)(x^3 +1)$

$= (2x^5 +2x^2 -3x^3 -3)$

$=$$2x^5 -3x^3 +2x^2 -3$

For f(-2), put x= -2

$f(-2) = 2(-2)^5 -3(-2)^3 +2(-2)^2 -3$

$= -64 +24 +8 -3$

$= -35$

So f(-2) = -35