Respuesta :

alessandroarenas

[tex]4x^4 +7x^2 -2=0\\16x^4 +7(4)x^2 -8\\(4x^2 +8)(4x^2-1)=0\\(x^2+2)(4x^2-1)=0\\x^2 + 2 =0 \vee 4x^2-1 = 0[/tex]


[tex]x^2+2 = 0[/tex]

Only has solutions in the complex numbers.

[tex]x= \sqrt{-2} \\x = \pm i \sqrt{2}[/tex]

And

[tex]4x^2-1 = 0\\x^2 = \frac{1}{4}\\x = \pm \frac{1}{2}[/tex]

MrRoyal

The factored form of the polynomial expression [tex]\mathbf{4x^4 + 7x^2 - 2 = 0}[/tex] is [tex]\mathbf{(4x^2 -1) ( x^2 + 2) = 0}[/tex]

The polynomial expression is given as:

[tex]\mathbf{4x^4 + 7x^2 - 2 = 0}[/tex]

Expand

[tex]\mathbf{4x^4 + 8x^2 - x^2 - 2 = 0}[/tex]

Factorize the expression

[tex]\mathbf{4x^2(x^2 + 2) -1( x^2 + 2) = 0}[/tex]

Factor out x^2 + 2

[tex]\mathbf{(4x^2 -1) ( x^2 + 2) = 0}[/tex]

Hence, the factored form of [tex]\mathbf{4x^4 + 7x^2 - 2 = 0}[/tex] is [tex]\mathbf{(4x^2 -1) ( x^2 + 2) = 0}[/tex]

Read more about factored form of polynomials at:

https://brainly.com/question/9972555

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