Answer:
Step-by-step explanation:
I am assuming 1 and 2 are asking for factors,
I am only gonna solve 4 for the sake of time,
9x^5-x^3+2x^2-x
x(9x^4-x^2+2x-1)
x(9x^4-(x^2-2x+1)
x(9x^4-(x-1)^2)
x(3x^2+x-1)(3x^2-x+1)
x^4+2x^2-24
x^4+6x^2-4x^2-24
x^2(x^2+6)-4(x^2+6)
(x^2-4)(x^2+6)
(x+2)(x-2)(x^2+6)
a^4+a^2+1
a^4+1+a^2
(a^2+1)^2-2a^2+a^2
(a^2+1)^2-a^2
(a^2+1-a)(a^2+1+a)
(a^2+a+1)(a^2-a+1)
a^3+b^3+c^3-3abc
=(a+b)^3+c^3−3ab(a+b)−3abc
=(a+b+c)^3−(3c(a+b)^2+3(a+b)c^2)−3ab(a+b+c)
=(a+b+c)^3−3c(a+b)(a+b+c)−3ab(a+b+c)
=(a+b+c)^3−(a+b+c)(3ab+3bc+3ac)
=(a+b+c)(a^2+b^2+c^2+2ab+2bc+2ac)−(a+b+c)(3ab+3bc+3ac)
=(a+b+c)(a^2+b^2+c^2−ab−bc−ac)
