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What is the completely factored form of this polynomial? x4 − 8x2 + 16 A. (x + 2)2(x − 2)2 B. (x2 − 4)2 C. (x2 + 4)(x + 2)(x − 2) D. (x + 2)(x − 2)

Sagot :

MrRoyalidn

The factored expression of x^4 - 8x^2 + 16 is  (x - 2)^2(x + 2)^2

How to factor the polynomial?

We have:

x^4 - 8x^2 + 16

Express -8x^2 as -4x^2 - 4x^2

x^4 --4x^2 - 4x^2 + 16

Factorize the expression

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

Factor out x^2 - 4

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

Express x^2 - 4 as difference of two squares

(x - 2)(x + 2)(x - 2)(x + 2)

Factorize the expression

(x - 2)^2(x + 2)^2

Hence, the factored expression of x^4 - 8x^2 + 16 is  (x - 2)^2(x + 2)^2

Read more about polynomials at:

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