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Select all factors of the following polynomial: 5p3 + 45p2 + 40p

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Select All Factors Of The Following Polynomial 5p3 45p2 40p class=

Sagot :

gmany

Answer:

[tex]\huge\boxed{5p;\ (p+1)}[/tex]

Step-by-step explanation:

[tex]5p^3+45p^2+40p=5p(p^2+9p+8)=5p(p^2+p+8p+8)\\\\=5p\bigg[p(p+1)+8(p+1)\bigg]=5p(p+1)(p+8)\\\Downarrow\\\boxed{5p};\ \boxed{(p+1)};\ \boxed{(p+8)}[/tex]

the factors for the given expression are

[tex]5p, p+1, p+8[/tex]

Given :

Given expression is [tex]5p^3 + 45p^2 + 40p[/tex]

Lets factor the given trinomial by factoring out GCF that is greatest common factor

Lets find out GCF from the given expression

all the terms are divisible by 5  and also we have 'p' in common

so GCf is 5p

[tex]5p^3 + 45p^2 + 40p\\5p\left(p^2+9p+8\right)\\[/tex]

Now we factor [tex]\left(p^2+9p+8\right)[/tex]

Product is 8  and sum is 9

So factors are 8  and 1

[tex]5p\left(p^2+9p+8\right)\\5p\left(p+1\right)\left(p+8\right)[/tex]

So the factors are

[tex]5p, p+1, p+8[/tex]

Learn more : brainly.com/question/20127500

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