SOLUTION: Use the Factor Theorem to determine whether the binomial x + 1 is a factor of the polynomial function �(x) = 2x3 � 9x2 + 13x � 6

Question 1108286: Use the Factor Theorem to determine whether the binomial x + 1 is a factor of the polynomial function �(x) = 2x3 � 9x2 + 13x � 6
Answer by ikleyn(52867) (Show Source): You can put this solution on YOUR website!
.

Based on the Factor theorem (whose correct name is the Remainder theorem), your alternative is THIS:


    - if (-1) IS     the root of the given polynomial, then (x+1) IS     the factor;

    - if (-1) IS NOT the root of the given polynomial, then (x+1) IS NOT the factor.


And you can easily check it on your own.

------------------
   Theorem   (the remainder theorem)
   1. The remainder of division the polynomial    by the binomial    is equal to the value    of the polynomial.
   2. The binomial    divides the polynomial    if and only if the value of    is the root of the polynomial , i.e. .
   3. The binomial    factors the polynomial    if and only if the value of    is the root of the polynomial , i.e. .

See the lessons
    - Divisibility of polynomial f(x) by a binomial (x-a) and the Remainder theorem
    - Solved problems on the Remainder thoerem
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

RELATED QUESTIONS
Use the factor theorem to decide whether the second polynomial is a factor of the first. (answered by stanbon)

Use the Factor Theorem to determine whether the first polynomial is a factor of the... (answered by josgarithmetic,stanbon)

Use synthetic division to determine whether x - c is a factor of the given polynomial. (answered by tommyt3rd)

Use the Factor Theorem to determine whether the first polynomial is a factor of the... (answered by ikleyn)

Use the Factor Theorem to determine whether the given binomial is a factor or not of... (answered by ikleyn)

Use the Factor Theorem to determine whether the first polynomial is a factor of the... (answered by Edwin McCravy)

Use the Factor Theorem to determine whether the first polynomial is a factor of the... (answered by josgarithmetic,MathTherapy)