Question

x^2+12x+27 divided by (x+3)​

Answer 1

Answer:

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sorry for the inconvenience. The second answer is the right solution

Answer 2

There are two methods to solve this question

1. Method of factorization

2. Method of Long Division

$\large\underline{\sf{Solution- \: method \: - 1}}$

$\rm :\longmapsto\:\dfrac{ {x}^{2} + 12x + 27}{x + 3}$

Using the concept of splitting of middle terms,

$\rm  \:  =  \: \:\dfrac{ {x}^{2} + 9x + 3x + 27}{x + 3}$

$\rm  \:  =  \: \:\dfrac{x(x + 9) + 3(x + 9)}{x + 3}$

$\rm  \:  =  \: \:\dfrac{(x + 3)(x + 9)}{x + 3}$

$\rm  \:  =  \: \:x + 9$

Hence,

$\bf :\longmapsto\:\dfrac{ {x}^{2} + 12x + 27}{x + 3} = x + 9$

$\large\underline{\sf{Solution- \: method \: - 2}}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{ \: \: \: \: \: \: \: \: x + 9 \: \: \: \: \: \: \: \: }}}\\ {\underline{\sf{x + 3}}}& {\sf{\: {x}^{2} + 12x + 27 \:\:}} \\{\sf{}}& \underline{\sf{  - {x}^{2} - 3x   \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {{\sf{}}}& {\sf{\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 9x + 27 \:  \:  \:  \:   \:  \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \:  \:  \:  \: \:  - 9x - 27\:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \: \:  \:0\:\:}}  \end{array}\end{gathered}\end{gathered}\end{gathered}$

Hence,

$\bf :\longmapsto\:\dfrac{ {x}^{2} + 12x + 27}{x + 3} = x + 9$

Additional Information :-

Splitting of middle terms :-

In order to factorize  ax² + bx + c we have to find numbers p and q such that p + q = b and pq = ac.

After finding p and q, we split the middle term in the given quadratic expression as px + qx and get the required factors by grouping the terms.