Question

HOW DO I FACTOR THESE POLYNOMIALS??

x^4+x^2- 12

a^4 + 6a^2 +5

X^4- 4x^2+3

x^4- 7x^2 +10

m^4+9m^2+20

x^4=8x^2+15

x^4+x^2-12

Answer 1

Ahhh ok so you can make the substitution:

\(x^2=y\) Then factor them normally, so I'll do the first one for you:

\(x^4+x^2- 12 \)
substitute
\(y^2+y-12\)
factor normally
\((y+4)(y-3)\)
substitute back in \(y=x^2\)
\((x^2+4)(x^2-3)\)
Then you can sometimes keep factoring the terms, but here I think you're pretty much stuck unless you want to have nonintegers or imaginary numbers,

\((x+2i)(x-2i)(x+\sqrt{3})(x-\sqrt{3})\)

So yeah, you will probably skip this last step :P

Answer 2

wot

Answer 3

where are you stuck

Answer 4

Ahhh ok so you can make the substitution:

Answer 5

you know that the objective is to find factors of the constant that adds up to the middle coefficient. rewrite the middle term with the components regroup, factor each group then use the distributive property to take out the common factor