Question

Anna made an error in determining the polynomial equation of smallest degree whose roots are -4,-2, -

and 2
Review Anna's work, identify the error and correct all work from that point forward that is affected by this error.
Include at least one sentence explaining her error. Use proper mathematical vocabulary, appropriately.

Answer 1

See explanation

Explanation:

Ana started the work nicely by multiplying out factors to get:\

`(x+4)(x+2)(2x+1)(x-2)=0`

She multiplied
`(x+2)(x-2)` correctly using difference of two squares to get:
`x^2-4`

Unfortunately: She made a mistake in multiplying
`(x+4)(2x+1)` she mistakenly got
`x^2+9x+4` instead of
`2x^2+9x+4`. She left out the coefficient of 2.

Therefore the second step should have been:

`(x^2-4)(2x^2+9x+4)`

The next step will now be:

`2x^4+9x^3+4x^2-8x^4-36x-16=0`

This simplifies to

`2x^4+9x^3-x^4-36x-16=0`