Question

factorize the expression and divide:
44 (p^4 -5p^3 -24p^2) ÷ 11p (p – 8)

Answer 1

Step-by-step explanation:

Given :-

44 (p^4 -5p^3 -24p^2) ÷ 11p (p – 8)

To find:-

factorize the expression and divide ?

Solution:-

Given that :-

44 (p^4 -5p^3 -24p^2) ÷ 11p (p – 8)

=> 44 [(p^2×p^2)-(5×p^2×p)-(24×p^2)÷ 11p(p-8)

=>44[p^2(p^2-5p-24)÷11p(p-8)

=>44p^2(p^2-5p-24)÷11p(p-8)

=>44p^2(p^2-8p+3p-24) ÷11p(p-8)

=>44p^2[p(p-8)+3(p-8)] ÷ 11p(p-8)

=>44p^2(p-8)(p+3) ÷ 11p(p-8)

=>4×11×p×p×(p-8)×(p+3) ÷ 11p(p-8)

=>11p(p-8)[4×p×(p+3)]÷11p(p-8)

On cancelling 11p(p-8) in both numerator and the denominator then

=>[4×p×(p+3)]

=>4p(p+3)

(or)

=>(4p×p)+(4p×3)

=>4p^2+12p

Answer:-

The answer for the given problem is 4p(p+3) or

4p^2+12p

Check:-

(4p^2+12p)×(11p (p – 8)

=>(4p^2+12p)(11p^2-88p)

=>4p^2×11p^2-4p^2×88p+12p×11p^2- 12p×88p

=>44p^4-352p^3+132p^3-1056p^2

=>44p^4-220p^3-1056p^2

=>44(p^4-5p^3-24p^2)

Verified the given relation

Used method :-

• Factorization Method

Answer 2

Answer:

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Step-by-step explanation:

Given

44(p⁴-5p³-24p²)÷ 22p ( p - 8)

To find

Factorize the expression and divide

Solution

Given that

44(p⁴-5p³-24p²)÷ 22p ( p - 8)

⇒44[(p²✕p²) - (5✕p² ✕p) - (24 ✕p²) ÷11p (p- 8)

⇒44 [ (p² - 5p - 24) ÷ 11p ( p - 8)

⇒44p² ( p² - 5p - 24) ÷ 11p ( p - 8)

⇒44p² ( p² - 8p + 3p - 24) ÷ 11p ( p-8)

⇒44p² [ P ( p - 8) +( p - 8)] ÷ 11p ( p - 8)

⇒44p² ( p - 8) ( p + 3) ÷ 11p ( p - 8)

⇒4 ✕ 11✕p✕p✕(p-8) ✕( p + 3) ÷ 11p (p-8)

⇒11p ( p- 8) [4✕p✕(p+3)]÷11p ( p - 8)

On cancelling 11p ( p - 8) in both numerator and the denominator then

⇒ [ 4 ✕p ✕ ( p + 3)

⇒4p ( p + 3)

Or

⇒(4p✕p)+(4p ✕3)

⇒4p² + 12p

Answer

The answer for the given problem is 4p (p +3) or 4p² + 12p

Check

(4p² + 12p) ✕( 11p(p - 8)

⇒(4p² + 12p)✕(11p² - 88p)

⇒4p²✕11p²-4p²✕88p+12p ✕11p² - 12p✕88p

⇒44p⁴-352p³+132p³-1056p²

⇒44p⁴-220p³ - 1056p²

⇒44(p⁴ - 5p³ - 24p²)

Verified the given relation