For a polynomial p(x), the value of p(3) is −2. Which of the following must be true about p(x)? (options in description)

2656 viewed last edited 5 years ago

Anonymous

1) x−5 is a factor of p(x).

2) x−2 is a factor of p(x).

3) x+2 is a factor of p(x).

4) The reminder when p(x) is divided by x−3 is−2.

I don't think there is sufficient information, but this was all that was there in the quesion

Vivekanand Vellanki (last edited 5 years ago) (Expert, Founder @Qalaxia)

Option 4 is correct.

Lets see how. Let's define a new polynomial f(x) = p(x) + 2.

Clearly, f(3) = p(3) + 2 = -2 + 2 = 0.

From reminder theorem, (x - 3) is a factor of f(x). This means that

f(x) = (x - 3)g(x)

p(x) + 2 = (x - 3)g(x); or

p(x) = (x - 3)g(x) - 2

So, when p(x) is divided by (x - 3), we get a reminder of -2.