Questions: 21p^6+30p^2+27

Solution Steps

To factor out the greatest common factor (GCF) from the expression \(21p^6 + 30p^2 + 27\), we need to identify the largest number that divides all the coefficients (21, 30, and 27) and the smallest power of \(p\) that is common to all terms.

To factor the expression \(21p^6 + 30p^2 + 27\), we first identify the greatest common factor (GCF) of the coefficients 21, 30, and 27. The GCF of these numbers is 3.

Next, we factor out the GCF from each term in the expression: \[ 21p^6 + 30p^2 + 27 = 3(7p^6) + 3(10p^2) + 3(9) \]

After factoring out the GCF, we simplify the expression inside the parentheses: \[ 3(7p^6 + 10p^2 + 9) \]

Final Answer