Show all work to factor x4 − 5x2 + 4 completely.

The factor of x⁴ - 5x² + 4 is (x - 1) (x + 1) (x-2) (x + 2) = 0

The factors of a polynomial are those values that if multiplied together they can be equal to the original value of the polynomial.

From the given information, the factor of x⁴ - 5x² + 4 can be determined using the difference of square.

Since both terms are perfect squares, the factors can be expressed by using the difference of square formula:

From

where;

∴

the factors of  x⁴ - 5x² + 4 can be expressed as(x - 1) (x + 1) (x-2) (x + 2) = 0 in the form a² - b² = (a+b) (a - b)

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(x^2-4)(x^2-1)

Step-by-step explanation:

Here, we want to factorize the given expression

x^4 - 5x^2 + 4

x^4 - x^2-4x^2 + 4

= x ^2(x^2 - 1)-4(x^2-1)

= (x^2-4)( x^2-1)

a² + b²= c²

24² + 7² = c²

c= 25