Solve 3x^5-87x^3+300x

$$3 x ^ { 5 } - 87 x ^ { 3 } + 300 x$$

Factor

$$3x\left(x-5\right)\left(x-2\right)\left(x+2\right)\left(x+5\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{5}-29x^{3}+100x\right)$$

Consider x^{5}-29x^{3}+100x. Factor out x.

$$x\left(x^{4}-29x^{2}+100\right)$$

Consider x^{4}-29x^{2}+100. Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{4} and m divides the constant factor 100. One such factor is x^{2}-25. Factor the polynomial by dividing it by this factor.

$$\left(x^{2}-25\right)\left(x^{2}-4\right)$$

Consider x^{2}-25. Rewrite x^{2}-25 as x^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5\right)\left(x+5\right)$$

Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$3x\left(x-5\right)\left(x+5\right)\left(x-2\right)\left(x+2\right)$$

Evaluate

$$3x\left(x^{4}-29x^{2}+100\right)$$