Question

Can someone check this comments below

Answer 1

Since you know that 'x-1' is one of the factors, you could use synthetic division to get the factored polynomial.

Answer 2

I'm going to assume you haven't done synthetic division, so I'll show ya.

Synthetic division is basically upside down long division but without dealing with variables.

For this one, we could use x=1 (from x-1=0)

Putting 1 on the left side. Then the numerical values for each variable in \( x^4-3x^3-19x^2+3x+18 \), which are 1, -3, -19, 3, and 18.

Answer 3

To start, you could bring the first value down, and multiply it by the one on the left.

Then move it back and add it to the second value. So 1*1 is 1, and move it back to add to -3. That gives -2, and so on. As shown here.

Answer 4

Ending in a zero means the polynomial factored out and left no remainders.
For the final factored answer, you just subtract 1 from the exponent and add back the variables.

So your answer would be \(\large \color{gold}{x^3-2x^2-21x-18 }\)