Finding All Zeros of a Polynomial Function Using The Rational Zero Theorem

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in this lesson we're going to focus on

the rational zero theorem this theorem

helps us to list all the possible

rational zeros of a polynomial function

so it's very useful when solving

polynomial equations so here's an

example let's say that f of X is equal

to 1 X cubed plus 2x squared minus 5x

minus 6 and let's list all of the

possible rational zeros so we need to

divide P by Q and P is associated with

the constant term Q is associated with

the leading coefficient so factors of P

or factors of negative 6 include plus or

minus 1 plus or minus 2 plus or minus 3

and plus or minus 6

now factors of the leading coefficient 1

is just plus or minus 1 and any number

divided by 1 is itself so therefore the

possible rational zeros are 1 2 3 & 6 so

if we set this function equal to 0 then