Question

question 9 of 10
difference of squares gives which complex factors for the expression ( x^2 + 3 )?

a. ( (x - isqrt{3})(x - isqrt{3}) )
b. ( (x + 3i)(x - 3i) )
c. ( (x + 3i)^2(x - 3i)^2 )
d. ( (x + isqrt{3})(x - isqrt{3}) )

Explanation:

Step1: Rewrite the expression

Rewrite $x^2 + 3$ as $x^2 - (i\sqrt{3})^2$ (since $i^2=-1$, so $(i\sqrt{3})^2=-3$).

Step2: Apply difference of squares

Use formula $a^2 - b^2=(a+b)(a-b)$ where $a=x$, $b=i\sqrt{3}$.
Result: $(x + i\sqrt{3})(x - i\sqrt{3})$.

Answer:

D. $(x + i\sqrt{3})(x - i\sqrt{3})$