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26 July, 18:39

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

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  1. 26 July, 18:51
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    The question is incomplete, the complete question is here

    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
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