Question

Can anyone give me a "hard" factoring polynomial equation? (If possible, the question can have the combination of factoring techniques.)

Answer 1

Okay, I'll give you a warming up one, factor this:
\[6a^2+14b-8-11ab+4b^2-8a\]

Answer 2

factor \(x^3 + 7x^2 + 14x +8\)

Answer 3

factor \(x^2-8x+17\) without using the quadratic formula or completing the square to find the roots first

Answer 4

cough cough \(x^2-2ax+a^2+b^2=(x-(a+bi))(x-(a-bi))\) so \(x^2-8x+17=x^2-8x+16+1=(x-(4+i))(x-(4-i))\)

Answer 5

also \(x^3+7x^2+14x+8=x^3+6x^2+8x+x^2+6x+8=(x+1)(x^2+6x+8)\\\quad\quad\quad=(x+1)(x+2)(x+4)\)