Question

Find the G.C.D. of the given polynomials

3x⁴ + 6x³ – 12x² – 24x, 4x⁴ + 14x³ + 8x² – 8x

Answer 1

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)]