Multiply the polynomials and simplify. $\begin{array} { r }
x ^ { 2 } + 5 x - 6 \
\times \quad 3 x + 4 \
\hline
\end{array}$
A) $3 x ^ { 3 } + 19 x ^ { 2 } + 5 x - 6$
B) $3 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 24$
C) $3 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 24$
D) $3 x ^ { 3 } + 4 x ^ { 2 } + 20 x - 6$
E) $3 x ^ { 3 } + 20 x ^ { 2 } - 6$

Question

Multiply the polynomials and simplify. $\begin{array} { r } 
x ^ { 2 } + 5 x - 6 \
\times \quad 3 x + 4 \
\hline
\end{array}$
A) $3 x ^ { 3 } + 19 x ^ { 2 } + 5 x - 6$
B) $3 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 24$
C) $3 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 24$
D) $3 x ^ { 3 } + 4 x ^ { 2 } + 20 x - 6$
E) $3 x ^ { 3 } + 20 x ^ { 2 } - 6$

Quizplus · Accepted Answer

Using distributivity of multiplication over addition, we get 
\begin{align*}
&(x^2 + 5x - 6) \cdot (3x + 4)\
&= x^2\cdot(3x)+x^2\cdot(4)+5x\cdot(3x)+5x\cdot(4)-6\cdot(3x)-6\cdot(4)\
&= 3x^3+4x^2+15x^2+20x-18x-24\
&= 3x^3+19x^2+2x-24
\end{align*} 
Therefore, the correct answer is (C).

Multiply the Polynomials and Simplify x2+5x−6×3x+4\begin{array} { r } x ^ { 2 } + 5 x - 6 \\\times \quad 3 x + 4 \\\hline\end{array}x2+5x−6×3x+4​​

Multiply the Polynomials and Simplify $\begin{array} { r } x ^ { 2 } + 5 x - 6 \\\times \quad 3 x + 4 \\\hline\end{array}$