Select the factors of x^2 − 14x + 49. (x + 49)(x + 1) (x + 7)(x + 7) (x − 7)(x − 7) (x − 49)(x − 1)

Question

Select the factors of x^2 − 14x + 49.

(x + 49)(x + 1)
(x + 7)(x + 7)
(x − 7)(x − 7)
(x − 49)(x − 1)

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Iris 12 hours 2021-09-11T06:19:24+00:00 1 Answer 0

Answers ( )

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    2021-09-11T06:20:59+00:00

    Answer: The third choice, (x-7)(x-7)

    Step-by-step explanation:

    (x+49)(x+1)\\(x+7)(x+7)\\(x-7)(x-7)\\(x-49)(x-1)\\

    Given, x^2-14x+49

    Let’s check the first one, 49x+x = 50x, not even right.

    The second one, 7x+7x = 14x, it’s wrong because it’s -14x and not 14x

    Third, -7x-7x = -14x which is right, (-7)(-7) = 49 which is right

    Fourth, -49x-x = -50x not right.

    Also for the second and third choices, you can convert it to perfect square

    (x+7)^2 \\(x-7)^2

    The formula of perfect square: ax^2+2(a)(b)(x)+b^2

    a = 1 and b = 7 so… From (x+7)^2

    x^2+2(1)(7)(x)+7^2 = x^2+14x+49

    While (x-7)^2

    x^2-2(1)(7)(x)+7^2 = x^2-14x+49

    So the answer is the third choice.

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