Question

Divide the polynomial (x² + 4x + 4) by the binomial (x + 2). What is the quotient and remainder?

Answer 1

quotient is X+2 and remainder is ,0

Answer 2

answer : remainder = 0 and quotient = (x + 2)

explanation : polynomial (x² + 4x + 4) is divided by another polynomial (x + 2).

we have to find quotient and remainder.

first of all, resolve (x² + 4x + 4) into simpler form,

x² + 4x + 4 = x² + 2.2.x + (2)²

we know, from algebraic identity, (a + b)² = a² + 2ab + b²

so, x² + 2.2.x + (2)² = (x + 2)²

now, (x² + 4x + 4) = (x + 2)² is divided by (x + 2)

i.e., (x + 2) ) (x + 2)² ( (x + 2)

(x + 2)²

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0

so, remainder = 0 and quotient = (x + 2)