Sure, let's factorize the expression [tex]\( 9p + 3 \)[/tex].
Step 1: Identify the greatest common factor (GCF).
- The terms in the expression are [tex]\( 9p \)[/tex] and [tex]\( 3 \)[/tex].
- The GCF of [tex]\( 9p \)[/tex] and [tex]\( 3 \)[/tex] is [tex]\( 3 \)[/tex], because 3 is the largest number that divides both 9 and 3.
Step 2: Factor out the GCF from each term.
- When we factor out the GCF [tex]\( 3 \)[/tex] from [tex]\( 9p \)[/tex], we are left with [tex]\( 3p \)[/tex] because [tex]\( 9p \div 3 = 3p \)[/tex].
- When we factor out the GCF [tex]\( 3 \)[/tex] from [tex]\( 3 \)[/tex], we are left with [tex]\( 1 \)[/tex] because [tex]\( 3 \div 3 = 1 \)[/tex].
Step 3: Write the expression as the product of the GCF and the simplified terms within parentheses.
- After factoring out the GCF [tex]\( 3 \)[/tex], the expression [tex]\( 9p + 3 \)[/tex] can be rewritten as [tex]\( 3(3p + 1) \)[/tex].
So, the factorized form of the expression [tex]\( 9p + 3 \)[/tex] is:
[tex]\[ \boxed{3(3p + 1)} \][/tex]
