Question

determine the product of linear and quadratic factors. verify graphically that the expressions are equivalent.
sample problem
$x(x^2 + 3x - 4)$
$x(x^2 + 3x - 4) = x^3 + 3x^2 - 4x$
the graph of the original expression and the graph of the final expression are the same. so the expressions are equivalent.

$(-2.3 + 1.1x + 0.9x^2)(4.5x - 3.8)$
type the answer in the space provided. use numbers instead of words.
$=\boxed{}$

Explanation:

Step1: Rearrange the quadratic factor

$(-2.3 + 1.1x + 0.9x^2) = (0.9x^2 + 1.1x - 2.3)$

Step2: Distribute linear term to quadratic

$0.9x^2(4.5x - 3.8) + 1.1x(4.5x - 3.8) - 2.3(4.5x - 3.8)$

Step3: Calculate each distributed term

$0.9\times4.5x^3 - 0.9\times3.8x^2 + 1.1\times4.5x^2 - 1.1\times3.8x - 2.3\times4.5x + 2.3\times3.8$
$= 4.05x^3 - 3.42x^2 + 4.95x^2 - 4.18x - 10.35x + 8.74$

Step4: Combine like terms

Combine $x^2$ terms: $-3.42x^2 + 4.95x^2 = 1.53x^2$
Combine $x$ terms: $-4.18x - 10.35x = -14.53x$

Answer:

$4.05x^3 + 1.53x^2 - 14.53x + 8.74$