Question

write each function as a sum using the fewest number of terms.
a. $p(x) = \left(-5x^3 + 3x^2 - 5\
ight) - \left(2x^2 + 4x\
ight)$
$p(x) = $
b. $q(x) = \left(-2x^2 + 3x\
ight)(2x + 4)$
$q(x) = $

Explanation:

Step1: Distribute the negative sign

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

Step2: Combine like $x^2$ terms

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

Step3: Apply distributive property (FOIL)

$q(x) = -2x^2(2x) + (-2x^2)(4) + 3x(2x) + 3x(4)$
$q(x) = -4x^3 - 8x^2 + 6x^2 + 12x$

Step4: Combine like $x^2$ terms

$q(x) = -4x^3 + (-8x^2 + 6x^2) + 12x$
$q(x) = -4x^3 - 2x^2 + 12x$

Answer:

a. $p(x) = -5x^3 + x^2 - 4x - 5$
b. $q(x) = -4x^3 - 2x^2 + 12x$