Which factored form is equivalent to 3p^3 + 27p^2 + 24p?

We have to find the factored form of the expression

Taking '3p' common from all the terms of the given expression, we get

= (Expression 1)

Now we will find the factors of the quadratic polynomial by middle term splitting method.

We will factorize it by finding two numbers whose sum is 9 and product is 8.

Therefore, 8 and 1 are the required numbers whose sum is 9 and product is 8.

Therefore, we will split the middle term in the expression 1.

=

Taking 'p' common from first two terms and '8' common from the last two terms.

=

Taking (p+1) common.

=

Therefore, the factored form of the given expression is .