Factoring Polynomials: does y^2 - 5y + 4 factor...?

[math_fanatic]

I'm having trouble solving this problem I need to factor the problem completely. However, if the polynomial is not factorable I have to write prime.

. . .y^2 - 5y + 4

I've been trying to do what my book has been showing me (which isn't a lot).

So far this is the work i've done on it

. . .y^2 - 5y +4
. . .1y^2-1y-4y+4
. . .(y^2-y)+(-4y+4)

From there I've become confused. I believe I messed up from the very first step I took. If anyone could tell me my error it would be a great help to me. Thanks!

math_fanatic

 

[tkhunny]

Re: Factoring Polynomials

y^2 - 5y +4
1y^2-1y-4y+4
(y^2-y)+(-4y+4)

Keep going.

y*(y-1)-4(y-1)

(y-4)*(y-1)

Get that Distributive stuff crammed in your head. You will need it over and over and over and...

 

[math_fanatic]

Re: Factoring Polynomials

y*(y-1)-4(y-1)

(y-4)*(y-1)

Get that Distributive stuff crammed in your head. You will need it over and over and over and...

So would the final answer be y^2+4, or what you had: (y-4)*(y-1)? This stuff has been confusing me for a long time.

 

[jonboy]

Re: Factoring Polynomials

so would the final answer be y^2+4 or what you had (y-4)*(y-1) This stuff has been confusing me for a long time.

Your factors are \(\displaystyle (y\,-\,4)\,(y\,-\,1)\) and your polynomial would be \(\displaystyle y^2\,-\,y\,-\,4y\,+\,4\,\to\,y^2\,-5y\,+\,4\)

\(\displaystyle \L \;y^2\,+\,4\) is incorrect because you forgot to FOIL the \(\displaystyle (y\,-\,4)\,(y\,-\,1)\) to get the middle term.

 

[math_fanatic]

Re: Factoring Polynomials

so would the final answer be y^2+4 or what you had (y-4)*(y-1) This stuff has been confusing me for a long time.

Your factors are \(\displaystyle (y\,-\,4)\,(y\,-\,1)\) and your polynomial would be \(\displaystyle y^2\,-\,y\,-\,4y\,+\,4\,\to\,y^2\,-5y\,+\,4\)

\(\displaystyle \L \;y^2\,+\,4\) is incorrect because you forgot to FOIL the \(\displaystyle (y\,-\,4)\,(y\,-\,1)\) to get the middle term.

Oooh! I see!! Thanks! I got it now! Thanks for the help! I finally got it.