Question:

Factor COMPLETELY: 5x4 - 65x2 +180?

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Factor COMPLETELY: 5x4 - 65x2 +180?

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  1. 5x4 - 65x2 +180

    5(13^4)X^2 +36

    x^4-13x^2+180


  2. 5x4 -- 65x2 + 180

    = 5(x^4 -- 13x^2 + 36)

    = 5(x^2 -- 4)(x^2 -- 9)

    = 5(x + 2)(x -- 2)(x + 3)(x -- 3)

  3. = 5x^4 - 65x^2 + 180

    = 5(x^4 - 13x^2 + 36)

    = 5(x² - 4)(x² - 9)

    = 5(x + 2)(x - 2)(x + 3)(x - 3)

    Answer: 5(x + 2)(x - 2)(x + 3)(x - 3)

  4. The answer is 70

    First, do 5x4. This equals 20.

    Then, do 65x2. This equals 130.

    Subtract 130 from 20. This equals -110.

    Lastly, add 180 to -110. This equals 20.

  5. factor out 5

    5(x4 - 13x2 + 36)

    perfect square trinomial

    5(x^2 - 9)(x^2 - 4)

    difference of squares

    5(x -3)(x + 3)(x -2)(x + 2)

  6. 5x^4-65x^2+180

    5(x^4-13x^2+36)

    5(x^2-9)(x^2-4)

    5(x-3)(x+3)(x-2)(x+2)

  7. 5x4 - 65x2 +180?

    5x4=20

    65x2=130

    20- neg130= neg.110

    neg.110+pos.180=70

  8. I am reading this as :-

    5x^4 - 65x² + 180

    5 (x^4 - 13 x² + 36)

    5 ( x² - 9 ) ( x² - 4 )

    5 (x - 3) (x + 3) (x - 2) (x + 2)

  9. 20-130+180=70

  10. 5x4 - 65x2 + 180

    => 5x2(x2- 13x + 36)

    => 5x2(x-9)(x-4)

  11. the expression is

    5[x^4-13x^2+36]

    =5 [k^2-13k+36]  where k=x^2

    =5 [k^2-9k-4k+36]

    =5[k(k-9)-4(k-9)]

    =5(k-9)(k-4)

    put k=x^2

    =5(x^2-9)(x^2-4)   now apply x^2-y^2=(x+y)(x-y)

    =5(x+3)(x-3)(x+2)(x-2) ans

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