Find the indicated product by applying the distributive property and combining similar terms. $( x + 8 ) \left( x ^ { 2 } - 6 x - 3 \right)$
A) $x ^ { 3 } + 2 x ^ { 2 } - 51 x - 24$
B) $x ^ { 3 } + 2 x ^ { 2 } - 51 x - 8$
C) $x ^ { 3 } + 8 x ^ { 2 } - 51 x - 24$
D) $x ^ { 3 } + 2 x ^ { 2 } - 48 x - 24$
E) none of these

Question

Quizplus · Accepted Answer

To find the product, distribute each term in the first polynomial across the second polynomial: $x(x^2) + x(-6x) + x(-3) + 8(x^2) + 8(-6x) + 8(-3)$. Simplifying, we get $x^3 - 6x^2 - 3x + 8x^2 - 48x - 24$, which combines to $x^3 + 2x^2 - 51x - 24$.

Find the Indicated Product by Applying the Distributive Property and Combining