Division of Polynomial by Monomial

Division of polynomial by monomial = divide each term of a polynomial by the monomial and simplify.

For dividing a polynomial in one variable by a monomial in the same variable, we perform the following steps :

• Obtain the polynomial(Dividend) and the monomial(divisor).
• Arrange the terms of the dividend in the descending order of their exponents.
• Separate the each term using heart method.
• Divide each term of the polynomial be the given monomial by using the rules of division of a monomial by a monomial.

Some solved examples:


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2) 9m⁵ + 12m⁴ - 6m² ÷ 3m²

Solution :
   9m⁵ + 12m⁴ - 6m²
= -------------------
         3m²
Separate each term using heart method

= (9m⁵/3m²) + (12m⁴/3m²) - (6m²/3m²)
= 3m³ + 4m² - 2
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3) 24x³y + 20x²y² - 4xy ÷ 2xy

Solution :
   24x³y + 20x²y² - 4xy
= --------------------
        2xy

= (24x³y/2xy) + (20x²y²/2xy) - (4xy/2xy)
= 12x² + 10xy - 2
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4) x + 2x² + 3x⁴ - x⁵ ÷ by 2x

Solution :
First arrange all the terms in decreasing order of exponents
-x⁵ + 3x⁴ + 2x² + x ÷ 2x

   -x⁵ + 3x⁴ + 2x² + x
= --------------------
        2x
= (-x⁵/2x) + (3x⁴/2x) + (2x²/2x) + (x/2x)

= (-1/2) x⁴ + (3/2)x³ + x + 1/2
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5) 5x² - 25x ÷ 5x

Solution :
First arrange all the terms in decreasing order of exponents
5x² - 25x ÷ 5x

    5x( x - 5)
= ------------
          5x
= x -5

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Division of Algebraic Expressions

• Division of Polynomial by Monomial
• Division of Polynomial by Binomial

Algebraic Expression Page

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