Dividing polynomial by monomial

Chapter 12 Class 8 Factorisation
Concept wise

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Ex 12.3, 2 (Method 1) Divide the given polynomial by the given monomial. (iii) 8 (π₯^3 π¦^2 π§^2 +π₯^2 π¦^3 π§^2 + π₯^2 π¦^2 π§^3) Γ· 4π₯^2 π¦^2 π§^2 8 (π₯^3 π¦^2 π§^2 +π₯^2 π¦^3 π§^2 + π₯^2 π¦^2 π§^3) = 8 (π₯Γπ₯^2 π¦^2 π§^2) + (π¦ Γ π₯^2 π¦^2 π§^2) + (z Γ π₯^2 π¦^2 π§^2) Taking π₯^2 π¦^2 π§^2 common = 8π₯^2 π¦^2 π§^2 (π₯ + y +z) Dividing (8 (π₯^3 π¦^2 π§^2 + π₯^2 π¦^3 π§^2 + π₯^2 π¦^2 π§^3))/(4π₯^2 π¦^2 π§^2 ) = (8γ π₯γ^2 π¦^2 π§^2 (π₯ + π¦ + π§))/(4π₯^2 π¦^2 π§^2 ) = 8/4 Γ (π₯^2 π¦^2 π§^2)/(π₯^2 π¦^2 π§^2 ) Γ (π₯ + y + z) = 2 Γ (π₯ + y + z) = 2 (π + y + z) Ex 12.3, 2 (Method 2) Divide the given polynomial by the given monomial. (iii) 8 (π₯^3 π¦^2 π§^2 +π₯^2 π¦^3 π§^2 + π₯^2 π¦^2 π§^3) Γ· 4π₯^2 π¦^2 π§^2 8 (π₯Γπ₯^2 π¦^2 π§^2) + (π¦ Γ π₯^2 π¦^2 π§^2) + (z Γ π₯^2 π¦^2 π§^2) = (8 (π₯^3 π¦^2 π§^2 + π₯^2 π¦^3 π§^2 + π₯^2 π¦^2 π§^3))/(4π₯^2 π¦^2 π§^2 ) = (8π₯^3 π¦^2 π§^2)/(4π₯^2 π¦^2 π§^2 ) + (8π₯^2 π¦^3 π§^2)/(4π₯^2 π¦^2 π§^2 ) + (8π₯^2 π¦^2 π§^3)/(4π₯^2 π¦^2 π§^2 ) = 2π₯ + 2y + 2z Taking (x + y + z) common = 2 (π + y + z)