Solve -4x^46x^2+3

$$-4 { x }^{ 4 } 6 { x }^{ 2 } +3$$

Evaluate

$$3-24x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-4x^{6}\times 6+3$$

Multiply -4 and 6 to get -24.

$$-24x^{6}+3$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(-8x^{4}x^{2}+1\right)$$

Consider -8x^{6}+1. Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -8x^{6} and n divides the constant factor 1. One such factor is 2x^{2}-1. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -4x^{4}-2x^{2}-1,2x^{2}-1.

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