The length of a rectangle is 14 inches, and its area is (+) square inches. Factor the expression for the area.

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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

Step-by-step 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