Question

God of mathematics solve it..........

Answer 1

Answer:

Remainder = 1

[ Refer to the attachment ]

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When we divide a number, for example, 25 by 5 we get 5 as quotient and 0 as the remainder. This can be expressed as:

Dividend = (Divisor × Quotient) + Remainder

i.e, 25= (5 x 5) + 0

Here the remainder is zero thus we can say 5 is a factor of 25 or 25 is a multiple of 5. Thus reminder gives us a link between dividend and the divisor. We can divide a polynomial by another polynomial and can express in the same way.

Let’s divide a polynomial, p(x) = 4x2 + x – 1 by another polynomial (x + 1). After a long division we will get quotient, q(x) = 4x-3 and remainder, r(x) = 2. This can be expressed as:

➡4x² + x – 1=(x + 1) × (4x-3) + 2

Suppose p(x) and g(x) are two polynomials where the degree of p(x) > g(x) and g(x) ≠0. When we divide p(x) by g(x), if we get the polynomial q(x) as quotient and r(x) as remainder, then this can be expressed as:

➡ p(x) = g(x) × q(x) + r(x)