Question

use what you know about addition and subtraction of polynomials to find the missing term represented by the question mark in each equation.
$(-4x^{2}+6x + 3)+(8x + 5+?)=2x^{2}+14x + 8$
? =
$(-b^{3}+3b^{2}+8)-(? - 5b^{2}-9)=5b^{3}+8b^{2}+17$
? =

Explanation:

Step1: Isolate the first unknown term

Let $? = P(x)$. Rearrange the first equation:
$P(x) = (2x^2 + 14x + 8) - (-4x^2 + 6x + 3) - (8x + 5)$

Step2: Simplify the first expression

Distribute the negative sign and combine like terms:
$P(x) = 2x^2 + 14x + 8 + 4x^2 - 6x - 3 - 8x - 5$
$P(x) = (2x^2 + 4x^2) + (14x - 6x - 8x) + (8 - 3 - 5)$
$P(x) = 6x^2 + 0x + 0 = 6x^2$

Step3: Isolate the second unknown term

Let $? = Q(b)$. Rearrange the second equation:
$Q(b) = (-b^3 + 3b^2 + 8) - (5b^3 + 8b^2 + 17) + 5b^2 + 9$

Step4: Simplify the second expression

Distribute the negative sign and combine like terms:
$Q(b) = -b^3 + 3b^2 + 8 - 5b^3 - 8b^2 - 17 + 5b^2 + 9$
$Q(b) = (-b^3 - 5b^3) + (3b^2 - 8b^2 + 5b^2) + (8 - 17 + 9)$
$Q(b) = -6b^3 + 0b^2 + 0 = -6b^3$

Answer:

First missing term: $6x^2$
Second missing term: $-6b^3$