Algebra-2

According to the Rational Root Theorem, if a polynomial equation has a rational root , then is a factor of the constant term and is a factor of the leading coefficient.

 

For the equation , the leading coefficient is 7 and the constant term is 10.

 

The factors of 7 are .

The factors of 10 are .

 

So the possible rational roots are .

 

Let's start testing these possible roots. Try .

Substituting into the equation:

=7 + 2 - 19 + 10

=9 - 19 + 10

=-10 + 10

=0

So is a root.

 

Using synthetic division to divide the polynomial by :

1 | 7   2   -19   10

  |       7    9   -10

  | 7    9   -10   0

So the equation becomes

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