Question

What is a polynomial function in standard form with zeros 1, -1, 2, and 4?

A. y=x^4-6x^3+7x^2+6x-8
B. y=x^4-6x^3+9x^2+6x-8
C. y=x^3+7x^2+6x-8
D. x^4-x^3+x^2+x-8

I actually want help with how to solve this, I don't just want the answer. Fan + Medal to whoever can help the best :)

Answer 1

@Michele_Laino could you help with this one? xx

Answer 2

@pooja195

Answer 3

hint:
the requested polynomial function have to contain such factors:
\[\Large x - 1,\quad x + 1,\quad x - 2,\quad x + 4\]

Answer 4

so, please do this multiplication:
\[\Large \left( {x - 1} \right) \cdot \left( {x + 1} \right) \cdot \left( {x - 2} \right) \cdot \left( {x + 4} \right) = ...?\]
what do you get?

Answer 5

I'm still confused, i dont understand alegbra at all

Answer 6

i figured it out, it was A

Answer 7

I meant that the requested polynomial function can be written as below:
\[\Large y = \left( {x - 1} \right) \cdot \left( {x + 1} \right) \cdot \left( {x - 2} \right) \cdot \left( {x - 4} \right)\]

Answer 8

Now, if we compute the indicated products, we get:
\[\Large \begin{gathered}
y = \left( {x - 1} \right) \cdot \left( {x + 1} \right) \cdot \left( {x - 2} \right) \cdot \left( {x - 4} \right) = \hfill \\
\hfill \\
= \left( {{x^2} - 1} \right) \cdot \left( {{x^2} - 6x + 8} \right) = \hfill \\
\hfill \\
= {x^4} - 6{x^3} + 7{x^2} - 6x - 8 \hfill \\
\end{gathered} \]
so, your answer is right!
@explicitvogue