Use the Euclidean algorithm to compute the gcd of a(x) = 5x3 − 2x2 − 22x + 21 and b(x) = 5x4 − 7x3 + 15x2 − 21x in R[x]
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Step 1
Divide b by a to find the remainder. Compute b ÷ a: - Leading term: (5x^4)/(5x^3) = x. - Multiply a by x: x*a = 5x^4 − 2x^3 − 22x^2 + 21x. - Subtract: b − x*a = −5x^3 + 37x^2 − 42x. Now divide this by a again (since degrees equal 3): - Leading term: Show more…
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