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The length of a rectangle is 14 inches and it’s area is (42x + 56) square inches. Factor the expression for the area. Write an expression for the width
Answer:
The factorization of the expression of the area is 14(3x + 4)
The expression of the width is (3x + 4) inches
Explanation:
To factor an expression find the greatest common factor of the terms of the expression, then divide each term by it to find the reminder of the terms in the bracket
∵ The area of the rectangle = (42x + 56)
- Lets find the factors of 42 and 56
∵ 42 = 1 × 42 , 2 × 21 , 3 × 14 , 6 × 7
∴ The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
∵ 56 = 1 × 56 , 2 × 28 , 4 × 14 , 7 × 8
∴ The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
∵ The common factor of 42 and 56 are 1, 2, 7, 14
∵ The greatest one is 14
∴ The greatest common factor of 42 and 56 is 14
Divide each term of the expression of the area by 14
∵ 42x ÷ 14 = 3x
∵ 56 ÷ 14 = 4
∴ (42x + 56) = 14(3x + 4)
∴ The factorization of the expression of the area is 14(3x + 4)
∵ The length of the rectangle is 14 inches
∵ Area of a rectangle = length × width
∴ The width of the rectangle is (3x + 4) inches
∴ The expression of the width is (3x + 4) inches