Question

x² - 2x - 63
x² - 2x + 63
x² - 16x + 63
x² - 16x - 63

Explanation:

Step1: Assume the task is to factor a quadratic like \(x^2 - 2x - 63\) (taking the first one as an example). We need two numbers that multiply to \(-63\) and add to \(-2\).

Find two numbers: \( -9\) and \(7\) since \(-9\times7 = -63\) and \(-9 + 7=-2\).

Step2: Factor the quadratic using these numbers.

\(x^2 - 2x - 63=(x - 9)(x + 7)\)
(If the task was different, like identifying a correct quadratic for a root or something else, but since factoring is common here, we show factoring. For other quadratics, similar steps: for \(x^2 - 2x + 63\), discriminant \(b^2 - 4ac=4 - 252=-248<0\), doesn't factor over reals. For \(x^2 - 16x + 63\), numbers \(-7\) and \(-9\) (since \(-7\times -9 = 63\), \(-7 + (-9)=-16\)), so \((x - 7)(x - 9)\). For \(x^2 - 16x - 63\), discriminant \(256+252 = 508\), not a perfect square, so factors with irrationals or over complex, but likely factoring over integers was intended for the first or third maybe.)

Answer:

For \(x^2 - 2x - 63\), factored form is \((x - 9)(x + 7)\); for \(x^2 - 16x + 63\), factored form is \((x - 7)(x - 9)\) (depending on the specific question, but showing factoring as a common task here).