Question

1. Find the G.C.D of x³-10x²+31x-30 and 2x³- 8x²+2x+12.

Answer 1

Answer:

x3+10x2+31x+30

=x3+2x2+8x2+16x+15x+30

=x2(x+2)+8x(x+2)+15(x+2)

=(x+2)(x2+8x+15)

=(x+2){x2+5x+3x+15}

=(x+2){x(x+5)+3(x+5)}

=(x+2)(x+3)(x+5)