Question

Please help me with this problem for my son to understand thank you.Factor completely.36x^4+18x^3+40x^2Enter your answer in the box.

Answer 1

The expression is given to be:

`36x^4+18x^3+40x^2`

Rewrite the terms so that we can factorize the common terms out:

`\begin{gathered} 36x^4\Rightarrow2x^2\cdot18x^2 \\ 18x^3\Rightarrow2x^2\cdot9x \\ 40x^2\Rightarrow2x^2\cdot20 \end{gathered}`

Therefore, the expression can be rewritten to be:

`2x^2\cdot18x^2+2x^2\cdot9x+2x^2\cdot20`

Since there is a common term, 2x², we can factorize to give:

`\Rightarrow2x^2(18x^2+9x+20)`

The quadratic function in the parentheses cannot be factored further.

Therefore, the answer is:

`2x^2(18x^2+9x+20)`