Question

4 which of the following expressions is a factor of the polynomial below? $7w^2 - 16w + 4$ a) $(7w + 4)$ peyton manning b) $(7w - 2)$ tony romo c) $(w + 1)$ tom brady d) $(w + 2)$ drew brees e) $(7w - 1)$ andrew luck

Explanation:

Step1: Factor the quadratic polynomial

We have the quadratic polynomial \(7w^2 - 16w + 4\). To factor it, we need to find two numbers that multiply to \(7\times4 = 28\) and add up to \(-16\). The numbers are \(-14\) and \(-2\) since \(-14\times(-2)=28\) and \(-14 + (-2)=-16\).

Rewrite the middle term using these numbers:
\(7w^2-14w - 2w + 4\)

Step2: Group and factor

Group the first two terms and the last two terms:
\((7w^2 - 14w)+(-2w + 4)\)

Factor out the greatest common factor from each group:
\(7w(w - 2)-2(w - 2)\)

Now, factor out the common binomial factor \((w - 2)\):
\((7w - 2)(w - 2)\)

So the factors of \(7w^2 - 16w + 4\) are \((7w - 2)\) and \((w - 2)\). Looking at the options, option B is \((7w - 2)\).

Answer:

B. \((7w - 2)\)