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Synthetic Division

To find the quotient and remainder when a polynomial is divided by a binomial.

Let

be a polynomial of the

So that,

Equating the coefficients of like powers of

Thus the coefficients

Let

**ƒ(x) = a**_{0}x^{n}+ a_{1}x^{n-1}+ …. + a_{n-1}x + a_{n}, a_{0}≠ 0 (1)be a polynomial of the

**n**^{th}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 ≡ b**_{0}x^{n-1}+ b_{1}x^{n-2}+ …. + b_{n-1}So that,

**a**_{0}x^{n}+ a_{1}x^{n-1}+ …. + a_{n}≡ (x – h) (b_{0}x^{n-1}+ b_{1}x^{n-2}+ …. + b_{n-1}) + R (2)Equating the coefficients of like powers of

**x**on both sides of the identity**(2)**, we getThus the coefficients

**b**_{0}, b_{1}, …., b_{n-1}and**R**are known.**Services: -**Synthetic Division Homework | Synthetic Division Homework Help | Synthetic Division Homework Help Services | Live Synthetic Division Homework Help | Synthetic Division Homework Tutors | Online Synthetic Division Homework Help | Synthetic Division Tutors | Online Synthetic Division Tutors | Synthetic Division Homework Services | Synthetic DivisionSubmit Your Query ???

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