Factor theorem, Algebra

Assignment Help:

Factor Theorem

For the polynomial P ( x ) ,

1. If value of r is a zero of P ( x ) then x - r will be a factor of P ( x ) .

2. If x - r is a factor of P ( x ) then r will be a zero of P ( x ) .

The factor theorem leads to the below fact.

Fact 1

If P ( x ) is a polynomial of degree n & r is a zero of P (x ) then P ( x ) can be written in the given form.

                                     P ( x ) = ( x - r ) Q (x )

Where Q (x) refer to a polynomial with degree n -1 .Q (x) can be found by dividing P (x) by x - r .

There is one more fact that we have to get out of the way.

Fact 2

If P ( x ) = ( x - r ) Q ( x )& x = t is a zero of Q ( x ) then x = t will also be a zero of P ( x ) .

This fact is simple enough to check directly.  First, if x = t is a zero of Q ( x ) then we know that,

                                                                      Q (t) = 0

As that is what it means to be a zero.  Thus, if x = t is to be a zero of P (x) then all we have to do is illustrates that P (t) =0 and that's in fact quite simple. Following it is,

P (t) = (t - r) Q (t) = (t - r) (0) = 0 and hence x = t is a zero of P (x).


Related Discussions:- Factor theorem

Algebra 1, 2x-3x=16 what do i do?.

2x-3x=16 what do i do?.

Pronumeral, A hotel places several small packs of butter on tables at break...

A hotel places several small packs of butter on tables at breakfast. The number of packs is given by the formula: b=3xg+1. B is the number of packs of butter, and g is the number

How do I solve, Suppose you are provided with a geometric sequence. How can...

Suppose you are provided with a geometric sequence. How can you find the sum of n terms of the sequence without having to add all of the terms?

Inaliz, i need help on the rate of change!!

i need help on the rate of change!!

Substitution method, i need to know the steps to 3x+4y=8 and -5x-3y=5 using...

i need to know the steps to 3x+4y=8 and -5x-3y=5 using the substitution method.

Set-builder notation, to get a discount at the diner, you must either be le...

to get a discount at the diner, you must either be less than 10 years old or at least 55 years old.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd