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Learning by Doing

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Objective: To factorise a polynomial of type px + qx + r (by splitting the middle
terms).

Materials Required: Chart paper, graph paper, scissors, sketch pens, and glue stick.
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Procedure: Let us consider a polynomial, say x + 5x + 6.
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• The polynomial can be expressed as x + 3x + 2x + 6 (by splitting the middle terms).
• Take a graph paper and cut a square of dimension x × x (say x = 6) from it, as shown in
the figure.

x

x 2 x

• Cut a rectangle of dimension x × 3 from graph paper, as shown in the figure.

x

3x 3

• Cut another rectangle of dimension x × 2 from graph paper, as shown in the figure.
x
2x 2

• Cut a rectangle of dimension 3 × 2 from graph paper, as shown in the figure.
3
2

• Arrange all the rectangles and square and paste them on a chart paper, as shown in the
figure.

x + 3

x 2 3x
x + 2

2x 6
• Find the area of shape formed.

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Observation: Here, area = x + 3x + ... + ... = x + 5x + 6. Also, area = (x + 3) ............... .
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Conclusion: From the above, we can conclude that the polynomial x + 5x + 6 = (x + 3)(x + 2).

Mathematics-8 310