How do you factor $3 x^{4} - 2 x^{2} - 1 = 0$ $3x^4-2x^2-1=0$ ?

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How do you factor $3 x^{4} - 2 x^{2} - 1 = 0$ $3x^4-2x^2-1=0$ ?

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Answer 1 · 2018-05-04T12:33:01

$(3 x^{2} + 1) (x - 1) (x + 1) = 0$ $(3x^2+1)(x-1)(x+1)=0$

Explanation:

$using the a-c method of factoring the quadratic in x^{4}$ $"using the a-c method of factoring the quadratic in "x^4$

$the factors of the product 3 \times - 1 = - 3$ $"the factors of the product "3xx-1=-3$

$which sum to - 2 are - 3 and + 1$ $"which sum to - 2 are - 3 and + 1"$

$split the middle term using these factors$ $"split the middle term using these factors"$

$3 x^{4} - 3 x^{2} + x^{2} - 1 \leftarrow factor by grouping$ $3x^4-3x^2+x^2-1larrcolor(blue)"factor by grouping"$

$= 3 x^{2} (x^{2} - 1) + 1 (x^{2} - 1)$ $=color(red)(3x^2)(x^2-1)color(red)(+1)(x^2-1)$

$take out the common factor (x^{2} - 1)$ $"take out the "color(blue)"common factor "(x^2-1)$

$= (x^{2} - 1) (3 x^{2} + 1)$ $=(x^2-1)(color(red)(3x^2+1))$

$x^{2} - 1 is a difference of squares$ $x^2-1" is a "color(blue)"difference of squares"$

$and factors in general as$ $"and factors in general as"$

$∙ x a^{2} - b^{2} = (a - b) (a + b)$ $•color(white)(x)a^2-b^2=(a-b)(a+b)$

$\Rightarrow x^{2} - 1 = (x - 1) (x + 1)$ $rArrx^2-1=(x-1)(x+1)$

$\Rightarrow 3 x^{4} - 2 x^{2} - 1 = (3 x^{2} + 1) (x - 1) (x + 1)$ $rArr3x^4-2x^2-1=(3x^2+1)(x-1)(x+1)$

Answer 2 · 2018-05-04T12:44:24

$(x - 1) (x + 1) (3 x^{2} + 1) = 0$ $(x-1)(x+1)(3 x^2+1)=0$

Explanation:

$3 x^{4} - 2 x^{2} - 1 = 0$ $3 x^4-2 x^2 -1 =0$ or

$3 x^{4} - 3 x^{3} + 3 x^{3} - 3 x^{2} + x^{2} - 1 = 0$ $3 x^4-3 x ^3 +3 x^3 -3 x^2 + x^2 -1 =0$ or

$3 x^{3} (x - 1) + 3 x^{2} (x - 1) + (x + 1) (x - 1) = 0$ $3 x^3(x-1)+3 x ^2(x-1)+ (x+1)(x-1)=0$ or

$(x - 1) (3 x^{3} + 3 x^{2} + x + 1) = 0$ $(x-1)(3 x^3+3 x ^2+ x+1)=0$ or

$(x - 1) {3 x^{2} (x + 1) + 1 (x + 1)} = 0$ $(x-1){3 x^2(x+1)+1( x+1)}=0$ or

$(x - 1) (x + 1) (3 x^{2} + 1) = 0$ $(x-1)(x+1)(3 x^2+1)=0$ [Ans]

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How do you factor $3 x^{4} - 2 x^{2} - 1 = 0$ $3x^4-2x^2-1=0$ ?

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How do you factor 3x4−2x2−1=03x^4-2x^2-1=0?

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How do you factor $3 x^{4} - 2 x^{2} - 1 = 0$ $3x^4-2x^2-1=0$ ?