Solve (9x^2+6x^4)+(2x^4-5x^2)

$$( 9 x ^ { 2 } + 6 x ^ { 4 } ) + ( 2 x ^ { 4 } - 5 x ^ { 2 } )$$

Evaluate

$$8x^{4}+4x^{2}$$

Solution Steps

Combine 6x^{4} and 2x^{4} to get 8x^{4}.

$$9x^{2}+8x^{4}-5x^{2}$$

Combine 9x^{2} and -5x^{2} to get 4x^{2}.

$$4x^{2}+8x^{4}$$

Factor

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

Solution Steps

Factor out x^{2}.

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

Consider 9+6x^{2}+2x^{2}-5. Multiply and combine like terms.

$$8x^{2}+4$$

Consider 8x^{2}+4. Factor out 4.

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

Rewrite the complete factored expression. Polynomial 2x^{2}+1 is not factored since it does not have any rational roots.

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