which value of a would make the following expression completely factored?\n$x^{2}-a$\n12\n36\n49\n81
which value of a would make the following expression completely factored?\n$x^{2}-a$\n12\n36\n49\n81
Answer
Explanation:
Step1: Recall difference - of - squares formula
The difference - of - squares formula is (x^{2}-y^{2}=(x + y)(x - y)). If (a) is a perfect square, the expression (x^{2}-a) can be factored further.
Step2: Analyze each option
- For (a = 12), since (\sqrt{12}=2\sqrt{3}), (12) is not a perfect square.
- For (a = 36), (\sqrt{36}=6), and (x^{2}-36=(x + 6)(x - 6)).
- For (a = 49), (\sqrt{49}=7), and (x^{2}-49=(x + 7)(x - 7)).
- For (a = 81), (\sqrt{81}=9), and (x^{2}-81=(x + 9)(x - 9)).
Answer:
A. 12