math

Match each polynomial in standard form to its equivalent factored form.

Standard forms:
8x^3+1
2x^4+16x
x^3+8

the equivalent equation that would match with it
(x+2)(x2−2x+4)
The polynomial cannot be factored over the integers using the sum of cubes method.
(2x+16)(4x^2−32x+64)
(x+1)(4x^2−2x+1)
2x(x+2)(x^2−2x+4)
(x+8)(x^2−16x+64)
(2x+1)(4x^2−2x+1)

For equation 1) 8x^3+1 I believe the matching product is (x+8)(x^2−16x+64)
For equation 2) (2x+16)I believe the matching product is (4x^2−32x+64)
For equation 3) x^3+8 I believe the matching product is (x+1)(4x^2−2x+1)

I am not really sure at all I am struggling with this subject

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  1. 8x^3+1 = (2x)^3 + 1^3 = ((2x)+1)((2x)^2 - (2x)(1) + 1^2)
    = (2x+1)(4x^2-2x+1)

    2x^4+16x = 2x(x^3+1) = 2x(x+1)(x^2-x+1)

    x^3+8 = x^3 + 2^3 = ...

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    oobleck
  2. would the third one be (x+2)(x2−2x+4)

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  3. or The polynomial cannot be factored over the integers using the sum of cubes method.

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  4. your factoring is correct.
    sum and difference of cubes can always be factored.

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    oobleck
  5. 2x^4+16x = 2x(x^3+1) = 2x(x+1)(x^2-x+1)
    Is not a choice I am confused.

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  6. Yeah I was looking at that and was wondering of I messed up some where

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