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 ->  Polynomials-and-rational-expressions -> 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)=      Log On


   

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) About Me  (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) About Me  (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 ======> t%285%29+=+5%5E3+-+5%285%29%5E2+-+9%285%29+%2B+45+=+0

Factoring: x%5E3+-+5x%5E2+-+9x+%2B+45, we get: 

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