Question

choose the correct values for a, b, c, and d that align like terms to find the sum vertically.
$1.3t^{3}+0.4t^{2}+(-24t)$
$+\quad a + \quad b + \quad c + \quad d$
$\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$
$\bigcirc \\ a=(-0.6t^{2}) \\ b=(-8) \\ c=18t \\ d=0t^{3}$
$\bigcirc \\ a=0t^{3} \\ b=(-0.6t^{2}) \\ c=18t \\ d=(-8)$
$\bigcirc \\ a=0t^{3} \\ b=(-0.6t^{2}) \\ c=(-8) \\ d=18t$
done

Explanation:

Step1: Identify term degrees

The first polynomial has terms: $1.3t^3$ (degree 3), $0.4t^2$ (degree 2), $-24t$ (degree 1). To add vertically, terms must align by degree, with a constant term (degree 0) as the remaining position.

Step2: Match positions to degrees

• Position A aligns with $1.3t^3$ (degree 3), so it must be $0t^3$ to match the degree.
• Position B aligns with $0.4t^2$ (degree 2), so it must be $-0.6t^2$ to match the degree.
• Position C aligns with $-24t$ (degree 1), so it must be $18t$ to match the degree.
• Position D is the constant term (degree 0), so it must be $-8$.

Answer:

A = $0t^3$ B = $(-0.6t^2)$ C = $18t$ D = $(-8)$