Question

if p(2) = 0 for polynomial p(x), then one factor of p(x) is............. ​

Answer 1

Answer:

its answer is 2

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Answer 2

If p(2) = 0

Then

g(x) = x + 2

Is a factor of p(x)

Just know one thing

Every Polynomial that is a factor of some Polynomial

Has to have same zeroes (Not necessarily equal number of zereos but atleast one zero

will be given by the factor

Like just let x + a be a factor of p(x) Polynomial

Then

Equate x + a = 0

x = -a

This will the zero the Polynomial

So p(-a) = 0

What we have done is just the reverse (starting from the final result p(-a) = 0)

Now if you are given p(-a) = 0 and the Polynomial this time is p(y)

Now

Here -a is the zero of p(y)

Since Polynomial and factor share a zero

So let a Polynomial g(y) have a zero -a

(Which gives g(-a) = 0)

now y + b = g(y) where b is a constant value (just like incase of g(y) = y + 5 or something else this is just an example)

when we put -a instead of y we get zero

So

g(-a) = -a + b = 0

b = a

Since b = a

Therefore the Polynomial must be

g(y) = y + a

And this was what I wanted you to understand

Hope this helps ☺️