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

$\left(a\right).\:\left(x+1\right)\left(x-2\right)\left(x+3\right)$

$\left(x\left(x-2\right)+1\left(x-2\right)\left(x+3\right)\right)$

$\left(x^2-2x+x+2\right)\left(x+3\right)$

$\left(x^2-x+2\right)\left(x+3\right)$

$x^3-x^2+2x+3x^2-3x+2\:$

$x^3+2x^2-x+2$

$at\:f\left(-2\right)=-2:$

$=\left(-2\right)^3+2\left(-2\right)^2-\left(-2\right)+2\:$

$=-8+8+2+2\:$

$=4$

$\left(b\right).\:\left(2x^2-3\right)\left(x^3+1\right)$

$2x^2\left(x^3+1\right)-3\left(x^3+1\right)$

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

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

$at\:f\left(x\right)=-2$

$=2\left(-2\right)^5+3\left(-2\right)^3+2\left(-2\right)^2-3$

$=-64-24+8-3$

$=-83$