synthetic division

I am not sure what is actually going on here, helping daughtet.

P(x)=4fortth - 7xthird + 66x - 72

Upside down division sign below.

4/ 1 -7 0 66 -72
-----------------
4 -12 -48 72
---------------
1 -3 -12 -48 72
-----------------

1 -3 -12 18 (o)=>4 is a zero of p(x)

xthird -3xsecond -12x + 18

1-3-12 18 I can't find a number that works here. I am not sure what I am supposed to be trying to do.

Quote:

---

Originally Posted by jonb

I am not sure what is actually going on here, helping daughtet.

P(x)=4fortth - 7xthird + 66x - 72

Upside down division sign below.

4/ 1 -7 0 66 -72
-----------------
4 -12 -48 72
---------------
1 -3 -12 -48 72
-----------------

1 -3 -12 18 (o)=>4 is a zero of p(x)

xthird -3xsecond -12x + 18

1-3-12 18 I can't find a number that works here. I am not sure what I am supposed to be trying to do.

---

is this your polynomial?

if P(x) = x^4 - 7x^3 + 66x - 72

yes

Quote:

---

Originally Posted by jonb

I am not sure what is actually going on here, helping daughtet.

P(x)=4fortth - 7xthird + 66x - 72

Upside down division sign below.

4/ 1 -7 0 66 -72
-----------------
4 -12 -48 72
---------------
1 -3 -12 -48 72
-----------------

1 -3 -12 18 (o)=>4 is a zero of p(x)

xthird -3xsecond -12x + 18

1-3-12 18 I can't find a number that works here.

try synthetic division with x = -3

---

...

ok...that worked. I am trying to figure out why this works.

thanks

Quote:

---

Originally Posted by jonb

ok...that worked. I am trying to figure out why this works.

thanks

---

why it works is the Rational Root Theorem.

Mathwords: Rational Root Theorem