The product of two polynomials is 3x4 + 5x3 — 21x2 — 53x — 30. If one of them is x2 — x — 6, find the other polynomial.

Question

Philoid · Accepted Answer

Here p(x) = the dividend polynomial = 3x⁴ + 5x³ — 21x² — 53x — 30

s(x) = the divisor polynomial = x² — x — 6

Now,

∴ The quotient polynomial q(x) = 3x² + 8x + 5 and the remainder polynomial r(x) = 0.

∴ The other polynomial is 3x² + 8x + 5.

The product of two polynomials is 3x⁴ + 5x³ — 21x² — 53x — 30. If one of them is x² — x — 6, find the other polynomial.