The expression is given to be:
[tex]36x^4+18x^3+40x^2[/tex]
Rewrite the terms so that we can factorize the common terms out:
[tex]\begin{gathered} 36x^4\Rightarrow2x^2\cdot18x^2 \\ 18x^3\Rightarrow2x^2\cdot9x \\ 40x^2\Rightarrow2x^2\cdot20 \end{gathered}[/tex]
Therefore, the expression can be rewritten to be:
[tex]2x^2\cdot18x^2+2x^2\cdot9x+2x^2\cdot20[/tex]
Since there is a common term, 2x², we can factorize to give:
[tex]\Rightarrow2x^2(18x^2+9x+20)[/tex]
The quadratic function in the parentheses cannot be factored further.
Therefore, the answer is:
[tex]2x^2(18x^2+9x+20)[/tex]
