athematics $10 C$
5
Assignment Booklet 3B
( 3 marks)
4. A rectangle has an area that can be represented by the expression $15 x^{2} + 30 x$ . The length and width can be found by factoring the expression. Write three possible expressions for the length and the width. Show complete factoring for each expression.
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\#2:
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Answer

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Answer

$3. Length: 5 x, Width: 3 (2 x + 1)$

Steps

Step 1 ：Find the greatest common factor (GCF) of the terms in the expression $15 x^{2} + 30 x$ . The GCF is 15.

Step 2 ：Factor out the GCF from the expression: $15 x^{2} + 30 x = 15 x (2 x + 1)$ .

Step 3 ：Find three possible expressions for the length and the width of the rectangle:

Step 4 ： $1. Length: 15 x, Width: (2 x + 1)$

Step 5 ： $2. Length: 3 x, Width: 5 (2 x + 1)$

Step 6 ： $3. Length: 5 x, Width: 3 (2 x + 1)$