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# Division of Algebraic Expressions - Division of a Polynomial by a Monomial

#### notes

Let us consider the division of the trinomial 4y^3 + 5y^2 + 6y by the monomial 2y.
4y^3 + 5y^2 + 6y = (2 × 2 × y × y × y) + (5 × y × y) + (2 × 3 × y)
we find that 2 × y is common in each term. Therefore, separating 2 × y from each term. We get
4y^3 + 5y^2 + 6y =2 × y × (2 × y × y) + 2 × y × (5/2 xx y) + 2 xx y xx 3

= 2y (2y^2) + 2y (5/(2 y)) + 2y(3)

= 2y (2y^2) + 2y (5/(2y))  2y(3)

= 2y (2y^2 + 5/(2 y) +3)    ...(the common factor 2y is shown separately).
Alternatively, we could divide each term of the trinomial by the monomial using the cancellation method.
(4y^3 + 5y^2 + 6y) ÷ 2y = (4y^3 + 5y^2 + 6y)/(2y)

= (4y^3)/(2y) + (5y^2)/(2y) + (6y)/(2y)

 = 2y^2 + 5/(2y) + 3

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Division of a Polynomial By a Monomial [00:06:58]
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