Divide the polynomials. Your answer should be in the form p(x)+\dfrac{k}{x+2}p(x)+ x+2 k p, left parenthesis, x, right parenthesis, plus, start fraction, k, divided by, x, plus, 2, end fraction where ppp is a polynomial and kkk is an integer. \dfrac{x^2+7x+12}{x+2}= x+2 x 2 +7x+12 =start fraction, x, squared, plus, 7, x, plus, 12, divided by, x, plus, 2, end fraction, equals

Step-by-step explanation:

Given

Required

Simplify and present your answer in

First, we need to expand and factorize the numerator:

Express 12 as 10 + 2

Split into two using brackets

Split to two fractions:

Factorize the numerator of the first fraction

The first fraction can be simplified to give:

Hence, by comparison:

We have simplified the given expression to the required format of:

Which implies that:

and

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step-by-step explanation: