Question

when asked to factor the trinomial $x^{2}-16x + 64$, a student gives the answer $(x - 8)(x + 8)$. which of the following statements is true? a. the answer is incorrect; the plus sign should be a minus sign. b. the answer is incorrect; the minus sign should be a plus sign. c. the answer is correct. d. the answer is incorrect; the trinomial cannot be factored.

Explanation:

Step1: Recall the perfect - square trinomial formula

The perfect - square trinomial formula is \(a^{2}-2ab + b^{2}=(a - b)^{2}\). For the trinomial \(x^{2}-16x + 64\), we have \(a=x\) and \(b = 8\) since \(2ab=2\times x\times8 = 16x\) and \(b^{2}=64\). So \(x^{2}-16x + 64=(x - 8)^{2}\).

Step2: Expand \((x - 8)(x + 8)\)

Using the difference - of - squares formula \((a - b)(a + b)=a^{2}-b^{2}\), when \(a=x\) and \(b = 8\), we get \((x - 8)(x + 8)=x^{2}-64\).

Answer:

A. The answer is incorrect; the plus sign should be a minus sign.