Question

question no 2 of assiment

Answer 1

here is your answer

common factor if p(x)1
150(6x^2+x-1)(x-3)^3
= 150(6x^2+3x-2x-1)(x-3)(x-3)(x-3)
150[3x(2x+1)-1(2x+1) ](x-3)(x-3)(x-3)
2×5×3×5×(3x-1)×(2x+1)×(x-3)×(x-3)×(x-3)

common factor of p(x)2
84(x-3)^2×(8x^2+14x+5)
2×2×3×7×(x-3)×(x-3)×(8x^2+10x+4x+5)
2×2×3×7×(x-3)(x-3)×[2x(4x+5)+1(4x+5)]
2×2×3×7×(x-3)(x-3)× (2x+1)(4x+5)

common factor in both thus polynomial
= 2×3×(x-3)(x-3)(2x+1)
so this is the HCF
6(x-3)^2×(2x+1)

hope this helps you
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