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adoni [48]
3 years ago
15

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

Mathematics
2 answers:
Andrej [43]3 years ago
6 0

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).

Anton [14]3 years ago
3 0
↪3p³+27p²+24p
=3p³+24p²+3p²+24p
=3p²(p+8)+3p(p+8)
=(p+8)(3p²+3p)
=3p(p+1)(p+8)➡ANS
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