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27 June, 11:47

Two students, Ann and Max, factored the trinomial 4x2-6x - 4. Ann factored it as 2 (k 2xx + 1) and Max factored it as (-2) 4x+2), Indicate which student factored the trinomial completely and which student did not, and explain why.

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  1. 27 June, 11:55
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    Given trinomial 4x^2-6x-4.

    In order to factor a trinomial, we need to factor out greatest common factor (GCF).

    In the given trinomial, we have terms 4x^2, - 6x, - 4.

    We can see that all terms can be divided by a greatest number 2.

    Therefore, greatest common factor would be 2 there.

    We need to factor out 2 first.

    On factoring out 2, we get

    2 (2x^2 - 3x - 2).

    Now, we need to factor out trinomial 2x^2 - 3x - 2 now.

    We can factor a trinomial by applying product sum rule.

    We have a=2, b=-3, c=-2.

    ac = 2*-2 = - 4 and b=-3.

    So, we need to find the factors of - 4 that add upto - 3.

    Factors of - 4 would be - 4 and 1.

    Let us replace - 3x by - 4x + 1x in 2x^2 - 3x - 2 trinomial

    2x^2 - 3x - 2 could be rewrite as 2x^2 - 4x + 1x - 2.

    Making it into two groups and factoring out GCF of each group.

    We get

    (2x^2 - 4x) + (1x - 2)

    2x (x-2) + 1 (x-2)

    = (x-2) (2x+1)

    Therefore, final factors of the trinomial is 2 (x-2) (2x+1).

    So, Ann factored form 2 (x-2) (2x+1) is correct.
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