To factor the expression 15x³ + 5x² + 6x² by grouping, we start by rearranging and combining like terms. Notice that the second and third terms can be combined:
15x³ + (5x² + 6x²) = 15x³ + 11x²
Next, we will group the terms:
(15x³) + (11x²)
Now, we can factor out the greatest common factor from each group. In the first group 15x³, we can factor out 5x²:
5x²(3x) + 11x²
Next, notice that 11x² can also be factored to get a common term, but since there’s no common factor with the first group directly, we rewrite it:
Thus, we factor again and look at 5x²(3x + 11)
The expression can’t be factored further because there are no common terms across both groups. Therefore, the resulting factored expression is:
5x²(3x + 11)
To summarize, by grouping and factoring, we have rewritten the polynomial 15x³ + 5x² + 6x² as 5x²(3x + 11).