Question

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What is remainder theorem?
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Answer 1

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Answer 2

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☃️ The Remainder Theorem begins with a polynomial say p(x) .

where,

• “p(x)” is some polynomial p whose variable is x .

✴️ Then as per theorem, dividing that polynomial p(x) by some linear factor x – a .

where,

• a is just some number .

☃️ Here we go through long polynomial division, which results in some polynomial q(x) (the variable “q” stands for “the quotient polynomial”) and a polynomial remainder is r(x) .

✴️ It can be expressed as:

• $\bf\red{\dfrac{p(x)}{x\:-\:a}\:=\:q(x)\:+\:r(x)\:}$

⭐ Remainder Theorem is an approach of Euclidean division of polynomials .

✈︎ According to this theorem,

• if we divide a polynomial P(x) by a factor (x – a), that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder .

• This remainder that has been obtained is actually a value of P(x) at x = a, specifically P(a) .

⚡ So basically, (x - a) is the divisor of P(x) if and only if P(a) = 0 . It is applied to factorize polynomials of each degree in an elegant manner .

☞ See the attachment diagram for example .

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