Hello I am asked the following: "Find the zeros algebraically".

y=4x^3+4x^2-7x+2

I know with the four terms I am supposed to group, however Grouping does not work with this problem. How do I factor this to find the zeros. Thanks.

Printable View

- Sep 6th 2010, 10:34 AMMack4545polynomial functions of Higher Degree
Hello I am asked the following: "Find the zeros algebraically".

y=4x^3+4x^2-7x+2

I know with the four terms I am supposed to group, however Grouping does not work with this problem. How do I factor this to find the zeros. Thanks. - Sep 6th 2010, 10:50 AMchisigma
Setting You obtain ... that means that contains as a factor... etc...

Kind regards

- Sep 6th 2010, 11:04 AMMack4545
- Sep 6th 2010, 11:27 AMchisigma
- Sep 6th 2010, 12:07 PMHallsofIvy
Very useful here is the "rational roots theorem":

**If m/n is a rational root of a polynomial equation with integer coefficients, then the numerator, m, must evenly divide the constant term and the denominator, n, must evenly divide the leading coefficient.**

Of course, that doesn't guarentee that there are**any**rational roots but it is always worth trying.

Here the leading coefficient is 4 so any rational root must have denominator , , or . The constant term is 2 so any rational root must have numerator or . That means that the only possible rational roots are , , , , , and . Trying each of those shows that only x= -2 really is a root.