Question

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

Answer 1

We have to find the factored form of the expression $3p^{3}+27p^{2}+24p$

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

= $3p(p^{2}+9p+8)$ (Expression 1)

Now we will find the factors of the quadratic polynomial $(p^{2}+9p+8)$ 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.

= $3p(p^{2}+p+8p+8)$

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

=$3p[p(p+1)+8(p+1)]$

Taking (p+1) common.

= $3p(p+1)(p+8)$

Therefore, the factored form of the given expression is $3p(p+1)(p+8)$.

Answer 2

↪3p³+27p²+24p
=3p³+24p²+3p²+24p
=3p²(p+8)+3p(p+8)
=(p+8)(3p²+3p)
=3p(p+1)(p+8)➡ANS