Question

add $(1.3t^{3}+0.4t^{2}-24t)+(8-18t+0.6t^{2})$
for each term in the second polynomial, enter the letter showing where that term should be placed to add the polynomials vertically.
$1.3t^{3}+0.4t^{2}+(-24t)$
+ a b c d
$\boldsymbol{\checkmark}=0.6t^{2}$
$\boldsymbol{\checkmark}=0t^{3}$
$\boldsymbol{\checkmark}=8$
$\boldsymbol{\checkmark}=-18t$
what is the sum of the polynomials?
$\bigcirc$ $1.3t^{3}+t^{2}-42t+8$
$\bigcirc$ $1.3t^{3}+t^{2}-6t+8$
$\bigcirc$ $1.9t^{3}+8.4t^{2}-42t$
$\bigcirc$ $1.9t^{2}-42t+8$
done
complete

Explanation:

Step1: Group like terms

Group terms by powers of $t$:
$$(1.3t^3) + (0.4t^2 + 0.6t^2) + (-24t - 18t) + (8)$$

Step2: Combine like terms

Calculate sums for each group:

• $t^3$ term: $1.3t^3$
• $t^2$ term: $0.4t^2 + 0.6t^2 = 1t^2 = t^2$
• $t$ term: $-24t - 18t = -42t$
• constant term: $8$

Step3: Assemble the polynomial

Combine the simplified terms:
$$1.3t^3 + t^2 - 42t + 8$$

Answer:

1.3$t^3$ + $t^2$ - 42$t$ + 8 (corresponding to the first option)