Solve (1)(x^5+1),(3-x^4),(4+x^3+x^6)

$$( 1 ) ( x ^ { 5 } + 1 ) , ( 3 - x ^ { 4 } ) , ( 4 + x ^ { 3 } + x ^ { 6 } )$$

Least Common Multiple

$$\left(x+1\right)\left(x^{4}-3\right)\left(x^{4}-x^{3}+x^{2}-x+1\right)\left(x^{6}+x^{3}+4\right)$$

Solution Steps

Factor the expressions that are not already factored.

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

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

$$\left(x+1\right)\left(x^{4}-3\right)\left(x^{4}-x^{3}+x^{2}-x+1\right)\left(x^{6}+x^{3}+4\right)$$

Expand the expression.

$$x^{15}+x^{12}-3x^{11}+x^{10}+4x^{9}-3x^{8}+x^{7}-3x^{6}-12x^{5}+4x^{4}-3x^{3}-12$$

Evaluate

$$x^{5}+1,3-x^{4},x^{6}+x^{3}+4$$