Dividing Polynomials

Kamis, 27 Juli 2023

In the previous lesson, you learned that some divisions can be performed using factoring.

          

Therefore, (x² + 4x + 3) ÷ (x + 3) = x + 1. Since the remainder is 0, the divisor is a factor of the dividend.

You can also use algebra tiles to model the division shown above.

You can also divide polynomials using long division. Follow these steps to divide 2x² + 7x + 3 by 2x + 1.

          

Therefore, (2x² + 7x + 3) ÷ (2x + 1) = x + 3.

 

Example

Find each quotient.

 

   

  

Therefore, (6y – 3) ÷ (2y – 1) = 3.

 

  

 

Therefore, (x² – 2x – 8) ÷ (x + 2) = x – 4.

 

If the divisor is not a factor of the dividend, the remainder will not be 0. The quotient can be expressed as follows.

Example

 

The quotient is 4y + 1 with remainder 2.

   

In an expression like x² – 4 there is no x term. In such situations, rename the dividend using zero as the coefficient of the missing term.

 

Example

 

   

 

If you know the area of a rectangle and the length of one side, you can find the width by dividing polynomials.

 

Example

Geometry Link

5.   Find the width of a rectangle if its area is 10x² + 29x + 21 square units and its length is 2x + 3 units.

 

Alternative Solutions:

 

To find the width, divide the area

10x² + 29x + 21 by the length 2x + 3.

  

 

Therefore, the width of the rectangle is 5x + 7 units. You can check your answer by multiplying (2x + 3) and (5x + 7).

 

 

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Labels: Mathematician

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