Question

Prove factor theoram,with proper explanation(please hurry),whoever gives me the perfect answer i will reward him as brainliest answer

Answer 1

The point of the Factor Theorem is the reverse of the Remainder Theorem: If you synthetic-divide a polynomial by x = a and get a zero remainder, then, not only is x = a a zero of the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor of the polynomial (courtesy of the Factor Theorem).

Just as with the Remainder Theorem, the point here is not to do the long division of a given polynomial by a given factor. This Theorem isn't repeating what you already know, but is instead trying to make your life simpler. When faced with a Factor Theorem exercise, you will apply synthetic division and then check for a zero remainder.

Ex Using the Factor Theorem, verify that x + 4 is a factor of
f (x) = 5x4 + 16x3 – 15x2 + 8x + 16.
If x + 4 is a factor, then (setting this factor equal to zero and solving) x = –4 is a root. To do the required verification, I need to check that, when I use synthetic division on f (x), with x = –4, I get a zero remainder:

completed division: 5 –4 1 4 0

The remainder is zero, so the Factor Theorem says that:

x + 4 is a factor of 5x4 + 16x3 – 15x2 + 8x + 16.


Hope it helps!
Pls mark as brainliest

Answer 2

Answer:

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