Solve x^3-3x+1,x^5+4x^3+x^2+3x+1

$$x ^ { 3 } - 3 x + 1 , x ^ { 5 } + 4 x ^ { 3 } + x ^ { 2 } + 3 x + 1$$

Least Common Multiple

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

Solution Steps

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$x^{8}+x^{6}+2x^{5}-9x^{4}+2x^{3}-8x^{2}+1$$

Evaluate

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