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

Transcript text: $21 p^{6}+30 p^{2}+27$

Solution

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.

Step 1: Identify the Greatest Common Factor (GCF)

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.

Step 2: Factor Out the GCF

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

Step 3: Simplify the Expression

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