Question

Factor the expression by grouping terms

$18x^3+9x^2+2x+1$

Short answer

The solution$18x^3+9x^2+2x+1=\left(9x^2+1\right)\left(2x+1\right)$

Step-by-step solution

Step 1. Apply the concept of distributive property.

If A, B and C are real numbers, then

$A\left(B+C\right)=\left(B+C\right)A=AB+AC$

Step 2. Analyze the expression.

Given$18x^3+9x^2+2x+1$

Let us consider first two terms,$18x^3,9x^2$

18, 9 have greatest common factor 9

$x^3,x^2$have greatest common factor$x^2$

So, the greatest common factor of the two terms is$x^2$

Step 3. Factor the polynomial.

Now, using the distributive property the polynomial can be factored as:

$\begin{array}{l}18x^3+9x^2+2x+1=\left(18x^3+9x^2\right)+2x+1\\ \Rightarrow 18x^3+9x^2+2x+1=9x^2\left(2x+1\right)+\left(2x+1\right)\\ \Rightarrow 18x^3+9x^2+2x+1=\left(9x^2+1\right)\left(2x+1\right)\end{array}$