Use a vertical format to find the product.
-$\begin{array} { r }
3 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 8 \
2 x + 5 \
\hline
\end{array}$
A) $25 x ^ { 4 } + 25 x ^ { 3 } + 35 x ^ { 2 } + 40 x$
B) $6 x ^ { 4 } + 15 x ^ { 3 } + 35 x ^ { 2 } + 42 x + 56$
C) $6 x ^ { 4 } + 25 x ^ { 3 } + 37 x ^ { 2 } + 46 x + 40$
D) $25 x ^ { 4 } + 35 x ^ { 3 } + 42 x ^ { 2 } + 56 x$

Question

Use a vertical format to find the product.
-$\begin{array} { r } 
3 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 8 \
2 x + 5 \
\hline
\end{array}$
A) $25 x ^ { 4 } + 25 x ^ { 3 } + 35 x ^ { 2 } + 40 x$
B) $6 x ^ { 4 } + 15 x ^ { 3 } + 35 x ^ { 2 } + 42 x + 56$
C) $6 x ^ { 4 } + 25 x ^ { 3 } + 37 x ^ { 2 } + 46 x + 40$
D) $25 x ^ { 4 } + 35 x ^ { 3 } + 42 x ^ { 2 } + 56 x$

Quizplus · Accepted Answer

When multiplying polynomials vertically, each term of the second polynomial is multiplied by each term of the first polynomial. For this problem, the correct product is $6x^4 + 25x^3 + 37x^2 + 46x + 40$, which matches option C. This is calculated by multiplying each term in $2x + 5$ by each term in $3x^3 + 5x^2 + 6x + 8$, and then adding the results together, aligning like terms.

Use a Vertical Format to Find the Product 3x3+5x2+6x+82x+5\begin{array} { r } 3 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 8 \\2 x + 5 \\\hline\end{array}3x3+5x2+6x+82x+5​​

Use a Vertical Format to Find the Product $\begin{array} { r } 3 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 8 \\2 x + 5 \\\hline\end{array}$