How do you factor $3 x^{2} + 36 x + 81$ $3x^2 + 36x + 81$ ?

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How do you factor $3 x^{2} + 36 x + 81$ $3x^2 + 36x + 81$ ?

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Answer 1 · 2016-05-16T17:15:20

$(3 x + 9) (x + 9)$ $(3x + 9 ) (x + 9 )$ is the factorised form of the expression.

Explanation:

$3 x^{2} + 36 x + 81$ $3x^2 + 36x + 81$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 3 \cdot 81 = 243$ $N_1*N_2 = a*c = 3* 81 = 243$

AND

$N_{1} + N_{2} = b = 36$ $N_1 +N_2 = b = 36$

After trying out a few numbers we get $N_{1} = 27$ $N_1 = 27$ and $N_{2} = 9$ $N_2 =9$
$27 \cdot 9 = 243$ $27*9 = 243$ , and $27 + (9) = 36$ $27+(9)= 36$

$3 x^{2} + 36 x + 81 = 3 x^{2} + 27 x + 9 x + 81$ $3x^2 + 36x + 81 = 3x^2 + 27x + 9 x+ 81$

$= 3 x (x + 9) + 9 (x + 9)$ $= 3x(x + 9 ) + 9 ( x + 9 )$

$(x + 9)$ $(x+9)$ is a common factor to each of the terms

$= (3 x + 9) (x + 9)$ $= (3x + 9 ) (x + 9 )$

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How do you factor $3 x^{2} + 36 x + 81$ $3x^2 + 36x + 81$ ?

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