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Home » Math Homework Help » Algebra Homework Help » Synthetic Division
Synthetic Division
To find the quotient and remainder when a polynomial is divided by a binomial.

Let ƒ(x) = a0xn + a1xn-1 + …. + an-1x + an, a0 ≠ 0                             (1)

be a polynomial of the nth degree. Let Q be the quotient and R be the remainder obtained when ƒ(x) is divided by the binomial (x – h). Surely, Q will be a polynomial of (n – 1)th degree. Let

Q ≡ b0xn-1 + b1xn-2 + …. + bn-1

So that,

a0xn + a1xn-1 + …. + an ≡ (x – h) (b0xn-1 + b1xn-2 + …. + bn-1) + R        (2)

Equating the coefficients of like powers of x on both sides of the identity (2), we get



Thus the coefficients b0, b1, …., bn-1 and R are known.

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