Question

question 4 of 10 when asked to factor the x^2 - 144, a student gives the answer (x - 12)(x - 12). what is the wrong with this answer? a. there is nothing wrong with the answer b. -1 is also a factor c. both minus signs should be plus signs d. one of the minus signs should be a plus sign

Explanation:

Step1: Recall difference - of - squares formula

The difference - of - squares formula is $a^{2}-b^{2}=(a + b)(a - b)$. In the expression $x^{2}-144$, we have $a = x$ and $b = 12$ since $144=12^{2}$. So $x^{2}-144=(x + 12)(x - 12)$.

Step2: Analyze the given answer

The given answer is $(x - 12)(x - 12)=(x - 12)^{2}=x^{2}-24x + 144$, which is not equal to $x^{2}-144$. The correct factoring should be in the form of a difference - of - squares, where one factor has a plus sign and the other has a minus sign.

Answer:

D. One of the minus signs should be a plus sign