SOLUTION: Show that the binomial is a factor of the polynomial. Then factor the polynomial completely. t(x)=x3−5x2−9x+45; x−5 t(x)=

Algebra.Com
Question 1058685: Show that the binomial is a factor of the polynomial. Then factor the polynomial completely.
t(x)=x3−5x2−9x+45; x−5
t(x)=
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Synthetic Division? The Factor Theorem? What result happens with these?

REVIEW The Rational Roots Theorem AND the Factor Theorem. What does the Factor Theorem mean?

What would be root if x-5 were a binomial factor of t? Root would be 5.
5    |     1    -5    -9    45
     |          5      0   -45
     |_______________________________
          1     0     -9    0

Now, YOU figure out what this tells you, and continue from there.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Show that the binomial is a factor of the polynomial. Then factor the polynomial completely.
t(x)=x3−5x2−9x+45; x−5
t(x)=
x - 5 is a FACTOR, so x - 5 = 0, and x = 5

If x - 5 is a factor, then t(5) MUST = 0. Does it? Check to see!

I'll give you a start ======> 

Factoring: , we get: 

It is that SIMPLE....nothing COMPLEX at all. 

RELATED QUESTIONS


Show that the binomial is a factor of the polynomial. Then factor the polynomial... (answered by stanbon)

Use synthetic division to show that g(x) is a factor of f(x), and complete the... (answered by josgarithmetic)

Use the factor theorem to show that 
x − c
 is a factor of f(x).
f(x) = x3 + x2... (answered by tommyt3rd)

Factor each polynomial completely given that the binomial following it is a factor of the  (answered by tutorcecilia)

Factor the polynomial completely.
 x3 -... (answered by ewatrrr)

 Consider the following.
x3 − kx2 + 2kx − 18
Find the value of k such that... (answered by josgarithmetic,MathLover1,MathTherapy)

Factor the polynomial and use the factored form to find the zeros. (Enter your answers as  (answered by lwsshak3)

This one is stumping me. Can anyone show me the steps and solution?

Factor each... (answered by Nate)

Factor each polynomial completely, given that the binomial following it is a factor of... (answered by venugopalramana)