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Question
Find the G.C.D. of the given polynomials
3x4 + 6x3 – 12x2 – 24x, 4x4 + 14x3 + 8x2 – 8x
Solution
p(x) = 3x4 + 6x3 – 12x2 – 24x
= 3x (x3 + 2x2 – 4x – 8)
g(x) = 4x4 + 14x3 + 8x2 – 8x
= 2x (2x3 + 7x2 + 4x – 4)
G.C.D. of 3x and 2x = x
Now g(x) is divide by p(x) we get
3x2 + 12x + 12 = 3 (x2 + 4x + 4)
Now dividing p(x) = x3 + 2x2 – 4x – 8
by the new remainder ...(leaving the constant)
x2 + 4x + 4
G.C.D. = x(x2 + 4x + 4) ...[Note x is common for p(x) and g(x)]
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