athematics $10 \mathrm{C}$
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.
\#1:
\#2:
\#3:
Answer
\(\boxed{\text{3. Length: } 5x, \text{ Width: } 3(2x + 1)}\)
Step 1 ：Find the greatest common factor (GCF) of the terms in the expression $15x^2 + 30x$. The GCF is 15.
Step 2 ：Factor out the GCF from the expression: $15x^2 + 30x = 15x(2x + 1)$.
Step 3 ：Find three possible expressions for the length and the width of the rectangle:
Step 4 ：\(\boxed{\text{1. Length: } 15x, \text{ Width: } (2x + 1)}\)
Step 5 ：\(\boxed{\text{2. Length: } 3x, \text{ Width: } 5(2x + 1)}\)
Step 6 ：\(\boxed{\text{3. Length: } 5x, \text{ Width: } 3(2x + 1)}\)
