Solve {l}{9x^{5}+7x^{4}+5x-21}{(3x^3-12+3x+4x^2)+(4x^3-4+4x-x^2)}

$$\left. \begin{array} { l } { 9 x ^ { 5 } + 7 x ^ { 4 } + 5 x - 21 } \\ { ( 3 x ^ { 3 } - 12 + 3 x + 4 x ^ { 2 } ) + ( 4 x ^ { 3 } - 4 + 4 x - x ^ { 2 } ) } \end{array} \right.$$

Least Common Multiple

$$\left(x-1\right)\left(7x^{3}+3x^{2}+7x-16\right)\left(9x^{4}+16x^{3}+16x^{2}+16x+21\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$9x^{5}+7x^{4}+5x-21=3\left(x-1\right)\left(3x^{4}+\frac{16}{3}x^{3}+\frac{16}{3}x^{2}+\frac{16}{3}x+7\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$7\left(x-1\right)\left(9x^{7}+\frac{139x^{6}}{7}+\frac{223x^{5}}{7}+\frac{128x^{4}}{7}+\frac{51x^{3}}{7}-\frac{81x^{2}}{7}-\frac{109x}{7}-48\right)$$

Expand the expression.

$$63x^{8}+76x^{7}+84x^{6}-95x^{5}-77x^{4}-132x^{3}-28x^{2}-227x+336$$

Evaluate

$$9x^{5}+7x^{4}+5x-21,\ 7x^{3}+3x^{2}+7x-16$$