Question

Factor.

Answer 1

Answer:

$(x+7i)(x-7i)$

Step-by-step explanation:

Since there is no middle term in the equation, one root must use addition (like a + b) while the other uses subtraction (like a – b) so they cancel one another and the middle term disappears. That would make the third term of the equation negative. However, in this instance, the third term is positive. Therefore, roots with imaginary units must be involved. Thus, $(x+7i)(x-7i)$ is the only solution. This is also true because the complex arithmetic rule results in the following:

$(a+bi)(a-bi)=a^2+b^2\\\rightarrow(x+7i)(x-7i)=x^2+7^2\\=x^2+49$