Solve {l}{16x^{4}-1}{3x^3+4x^2-13x+6}{4x^4-21x^2+5}

$$\left. \begin{array} { l } { 16 x ^ { 4 } - 1 } \\ { 3 x ^ { 3 } + 4 x ^ { 2 } - 13 x + 6 } \\ { 4 x ^ { 4 } - 21 x ^ { 2 } + 5 } \end{array} \right.$$

Least Common Multiple

$$\left(x-1\right)\left(3x-2\right)\left(x+3\right)\left(x^{2}-5\right)\left(16x^{4}-1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$16x^{4}-1=\left(2x-1\right)\left(2x+1\right)\left(4x^{2}+1\right) 3x^{3}+4x^{2}-13x+6=3\left(x-1\right)\left(3x-2\right)\left(\frac{1}{3}x+1\right) 4x^{4}-21x^{2}+5=\left(2x-1\right)\left(2x+1\right)\left(x^{2}-5\right)$$

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

$$\left(x-1\right)\left(2x-1\right)\left(3x-2\right)\left(x+3\right)\left(2x+1\right)\left(x^{2}-5\right)\left(4x^{2}+1\right)$$

Expand the expression.

$$48x^{9}+64x^{8}-448x^{7}-224x^{6}+1037x^{5}-484x^{4}+28x^{3}+14x^{2}-65x+30$$

Evaluate

$$16x^{4}-1,\ 3x^{3}+4x^{2}-13x+6,\ 4x^{4}-21x^{2}+5$$