Explanation:
we sadly need to do all the multiplications for the whole polynomial in standard form.
the other 3 things we get out of the given form :
we multiply 3 terms, each in x. the result will be x³.
so, we have the 3rd degree.
the leading coefficient is 1, as for the x³ term we get x×x×x = x³. no other number is involved.
the constant term is the extreme on the other end. it is 4×2×1 = 8.
so, now for the full multiplications, that should also show you, why I could make the conclusions above.
(x+4)(x-2)(x+1)
we do this by multiplying first 2 terms with each other, and then we multiply that result by the third term.
remember, we need to multiply every item of one term with every item in the other term.
(x+4)(x-2) = x² -2x + 4x - 8 = x² + 2x - 8
now
(x² + 2x - 8)(x+1) = x³ + x² + 2x² + 2x - 8x - 8 =
= x³ + 3x² - 6x - 8
so, that is already the standard form
f(x) = x³ + 3x² - 6x - 8