Solve 2x^4-20x^2+18

$$2 x ^ { 4 } - 20 x ^ { 2 } + 18$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(x^{4}-10x^{2}+9\right)$$

Consider x^{4}-10x^{2}+9. 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 9. One such factor is x^{2}-9. Factor the polynomial by dividing it by this factor.

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

Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$2\left(x^{4}-10x^{2}+9\right)$$