Question

the function $i(x)$ is the product of two polynomials.
$i(x) = \left(x^2 + 6\
ight)\left(-x^3 + 2x - 1\
ight)$
write $i(x)$ as a sum using the fewest number of terms.
$i(x) = $

Explanation:

Step1: Distribute $x^2$ to each term

$x^2(-x^3 + 2x - 1) = -x^5 + 2x^3 - x^2$

Step2: Distribute 6 to each term

$6(-x^3 + 2x - 1) = -6x^3 + 12x - 6$

Step3: Combine the two results

$(-x^5 + 2x^3 - x^2) + (-6x^3 + 12x - 6)$

Step4: Combine like terms

$-x^5 + (2x^3 - 6x^3) - x^2 + 12x - 6 = -x^5 - 4x^3 - x^2 + 12x - 6$

Answer:

$I(x) = -x^5 - 4x^3 - x^2 + 12x - 6$