Thread: How do you Square a polynomial?

1. How do you Square a polynomial?

Antiderivatives / Volumes - 5

click on Ex. number 2. They square the polynomial x^3 -x + 1.

I have tried FOIL, no luck though.

2. Hello. I am at school and the website is refusing to open for me but I will show you how to square the polynomial using the FOIL method.

The polynomial we are squaring is $\displaystyle x^3 -x + 1.$
In order to square something, we multiply it by itself. $\displaystyle (x^3 -x + 1)(x^3 -x + 1)$
All you do now is multiply each term in the first bracket by each term of the 2nd bracket so
$\displaystyle x^6-x^4+x^3-x^4+x^2-x+x^3-x+1$
Now we collect like terms
$\displaystyle x^6-2x^4+2x^3+x^2-2x+1$

3. Originally Posted by Math Blaster
They square the polynomial x^3 -x + 1.

I have tried FOIL, no luck though.
"FOIL" only works in the single context of multiplying two binomials. If either polynomial is not a binomial, then FOIL won't work.

To learn how to do this, try this lesson on multiplying polynomials.

Using the "vertical" method would probably work best, so, after studying the lesson and learning the general method, set up your exercise as:

[HTML]set-up:

x^3 - x + 1
x^3 - x + 1
------------------------[/HTML]
(Note how space was left for any "x-squared" terms that might crop up.) Then multiply from the right-hand side of the lower polynomial against the the upper polynomial. So the first step would be:

[HTML]first multiplication:

x^3 - x + 1
x^3 - x + 1
------------------------
x^3 - x + 1[/HTML]
Then multiply the "-x" through:

[HTML]second multiplication:

x^3 - x + 1
x^3 - x + 1
------------------------
x^3 - x + 1
-x^4 + x^2 - x[/HTML]
Do the last multiplication, draw another "equals" bar across the bottom, and then add down, to find your answer.