Question

Factor completely x² + 64

Answer 1

(b) Prime

Step-by-step explanation:

The difference of squares can be factored as ...

a² -b² = (a -b)(a +b)

This polynomial expression can be considered to be the difference of squares.

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For the squares x² and (-64), the linear factors will have constants equal to the root of -64, which is an imaginary number.

√(-64) = 8i

x² +64 = (x -8i)(x +8i)

This is the complete factorization.

However, the constants in this factorization are not integers. Hence we say this polynomial cannot be factored using integers.

When it cannot be factored using integers, it is considered prime.

Answer 2

B) Prime

Step-by-step explanation:

`\quad \large{\boxed{\sf x^2 +64}}`

The polynomial (x² + 64) is prime because it has only two factors.

Factors: 1 and (x² + 64)

Note: Prime polynomials are those whose factors are 1 and itself. Prime polynomials cannot be factored.