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Write a polynomial of least degree with roots $0$ and $-5$ . $\newline$ Write your answer using the variable $x$ and in standard form with a leading coefficient of $1$ . $\newline$ ______

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Write a polynomial from its roots

Full solution

Q. Write a polynomial of least degree with roots

0

and

-5

.

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

.

\newline

______

Root Correspondence: The root $0$ corresponds to the factor $x$ because if $x$ is $0$ , the expression equals $0$ .
Factor Calculation: The root $-5$ corresponds to the factor $(x - (-5))$ which simplifies to $(x + 5)$ .
Polynomial Multiplication: Now, we multiply the factors to get the polynomial: $x * (x + 5) = x^2 + 5x$ .
Standard Form Polynomial: The polynomial in standard form with a leading coefficient of $1$ is $x^2 + 5x$ .

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