How would I write this equation in standard form?

[vgamelover123]

I tried 5 times and no luck it gives a different format.

 

[Steven G]

You know by now that we do not solve problems for students.
Show us your work and we will inform you where you made any mistakes.

 

[R.M.]

Start by multiplying out your factors. Since you know that x = 1 [MATH]\pm[/MATH] i and x = 2 are roots, then what were those factors?

 

[vgamelover123]

You know by now that we do not solve problems for students.
Show us your work and we will inform you where you made any mistakes.

I did show my work in the other screencap but it gives me a different format

 

[Dr.Peterson]

I did show my work in the other screencap but it gives me a different format

You showed your answer, not your work; and the difference is not in the format, but the specific numbers.

Please show how you got your answer, so we can help you find your error.

 

[Steven G]

I did show my work in the other screencap but it gives me a different format

Do you really think that I will consider looking at every possible error that one can make until I figure out your error just because you chose not to show your work? I don't think so. Good luck.

 

[Otis]

I did show my [answer] in the [second screenshot] …

Hello vgamelover. Your answer for the second exercise suggests that you used 4±i instead of -4±i. Please try the second exercise again.

In the first exercise, we start by multiplying (x-2)(x-1-i)(x-1+i). Is that what you did?

If you'd like more help with the first exercise, then please post what you tried. Thanks!

?

 

[HallsofIvy]

A polynomial that has zeros at \(\displaystyle x= 1\pm i\) and \(\displaystyle x= 2\) must be a multiple of \(\displaystyle (x- 1- i)(x- 1+ i)(x- 2)\). To multiply \(\displaystyle (x- 1- i)(x- 1+ i)\) write it as \(\displaystyle ((x-1)- i)((x-1)+ i)\) and treat it as \(\displaystyle (a- b)(a+ b)= a^2- b^2\): \(\displaystyle (x- 1)^2- (i)^2= x^2- 2x+ 1- (-1)= x^2- 2x+ 2\). Multiply that by x-2. Finally, multiply by a constant to make f(0)= 4.