Solve 25-100x^4

$$25-100 { x }^{ 4 }$$

Factor

$$25\left(-2x^{2}-1\right)\left(2x^{2}-1\right)$$

Solution Steps

Factor out 25.

$$25\left(1-4x^{4}\right)$$

Consider 1-4x^{4}. Rewrite 1-4x^{4} as 1^{2}-\left(2x^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Reorder the terms.

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

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -2x^{2}+1,2x^{2}+1.

$$25\left(-2x^{2}+1\right)\left(2x^{2}+1\right)$$

Evaluate

$$25-100x^{4}$$