Question

please factorize it :- 4x³ + 12x² + 20x​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

Factorize:-

• $\sf\green{4 {x}^{3} \: + \: 12 {x}^{2} \: + \: 20x }$

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

• The greatest common factor of the numerical cofficients 4, 12 , and 20 is 4 .

• The greatest common factor of variables is x.

$\sf\red{So, \: 4x \:is \: the \: greatest \: common \: factor \: of \: given \: expression }$

$\qquad \quad {:} \longrightarrow \sf{\sf{Divide \: 4 {x}^{3} \: + \: 12 {x}^{2} \: + \: 20x \: by \: 4x }}$

$\qquad\quad {:} \longrightarrow \underline \blue{\boxed{\sf{( \: {x}^{2} \: + \: 3x \: + \: 5 \: ) }}}$

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$\large\underline{ \underline{ \sf \maltese{ \: Verification:- }}}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 4 {x}^{3} \: + \: 12 {x}^{2} \: + \: 20x \: = 4x(\:{x}^{2} \: + \: 3x \: + \: 5 )\: \\ \\ \\\end{gathered}\end{gathered}$

$\qquad\quad {:} \longrightarrow \underline \orange{\boxed{\sf{ \:4 {x}^{3} \: + \: 12 {x}^{2} \: + \: 20x \: = \: 4 {x}^{3} \: + \: 12 {x}^{2} \: + \: 20x \: }}}$

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Hence, Proved

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Factorization\:of \: given \: expression = \underline {\underline{4x( \: {x}^{2} \: + \: 3x \: + \: 5 \: ) }}}\\\end{gathered}\end{gathered}$

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$\large\underline{ \underline{ \sf \maltese{ \: Extra \: information:- }}}$

• The process of writing an algebraic expression as the product of two or more algebraic expression is called factorisation.

Methods of factorisation:-

1. Factorization by taking out a common factor.
2. Factorisation by using identities.
3. Factorisation by splitting the middle term of a quadratic expression to form ax² + bx + c

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