Question

If f(x)=8x^3+27 has a factor( 4x^2-6x+9) then its linear factor is

Answer 1

$\textbf{Given:}$

$f(x)=8x^3+27$

$\textbf{To find:}$

$\text{The linear factor of f(x)}$

$\textbf{Solution:}$

$\text{Consider,}$

$f(x)=8x^3+27$

$f(x)=(2x)^3+3^3$

$\text{Using the identity,}$

$\boxed{\bf\,a^3+b^3=(a+b)(a^2-ab+b^2)}$

$\text{We can factorize f(x) as}$

$f(x)=(2x+3)((2x)^2-(2x)(3)+3^2)$

$\bf\,f(x)=(2x+3)(4x^2-6x+9)$

$\therefore\textbf{The linear factor of \bf\,f(x) is \bf\,2x+3 }$

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