a)-6x²+7x-2=-6x²+4x+3x-2=-2x(3x-2)+(3x-2)=(-2x+1)(3x-2)
b)-5x²+16x-3=-5x²+15x+x-3=-5x(x-3)+(x-3)=(-5x+1)(x-3)
c)x²-4x-5x+20=x(x-4)-5(x-4)=(x-4)(x-5)
d)2x²-8x+3x-12=2x(x-4)+3(x-4)=(2x+3)(x-4)
a)x^4+4=x^4-4x²+4x²+4=(x^4+4x²+4)-4x²=(x²+2)²-4x²=(x²+2-4x)(x²+2+4x)
b)x^4+x^2+1=x^4+x^2+1+x-x=x(x³-1)+x²+x+1=x(x-1)(x²+x+1)+(x²+x+1)
=(x²+x+1)[x(x-1)+1]=(x²+x+1)(x²-x+1)
c)x^5+x+1=x^5-x²+x²+x+1=x²(x³-1)+x²+x²+x+1=x²(x-1)(x²+x²+x+1)+x²+x²+x+1
=(x²+x²+x+1)(x³-x²+1)
d)x^4+4y^4=(x²)²+4x²y²+(2y²)²-4x²y²=(x²+2y²)²-(2xy)²=(x²+2y²-2xy)(x²+2y²+2xy)