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Write a polynomial function of least degree with zeros $0$ , $1$ , $2$ , and $5$ . Write your answer using the variable $x$ and in standard form with a leading coefficient of $1$ . $f(x)=$

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Write a polynomial from its roots

Full solution

Q. Write a polynomial function of least degree with zeros

0

,

1

,

2

, and

5

. Write your answer using the variable

x

and in standard form with a leading coefficient of

1

.

f(x)=

Identify factor for zero $0$ : Step $1$ : Identify the factor for the zero $0$ . $\newline$ Factor: $(x - 0) = x$ .
Identify factor for zero $1$ : Step $2$ : Identify the factor for the zero $1$ . $\newline$ Factor: $(x - 1) = (x - 1)$ .
Identify factor for zero $2$ : Step $3$ : Identify the factor for the zero $2$ . $\newline$ Factor: $(x - 2) = (x - 2)$ .
Identify factor for zero $5$ : Step $4$ : Identify the factor for the zero $5$ . $\newline$ Factor: $(x - 5) = (x - 5)$ .
Multiply factors to get polynomial: Step $5$ : Multiply all factors to get the polynomial. $\newline$ $f(x) = x \cdot (x - 1) \cdot (x - 2) \cdot (x - 5)$ $\newline$ $= x(x - 1)(x - 2)(x - 5)$ $\newline$ $= x(x^3 - 8x^2 + 21x - 10)$ // Expanding the polynomial $\newline$ $= x^4 - 8x^3 + 21x^2 - 10x.$

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