Write a polynomial of least degree with roots -1 and -6. Write your answer using the variable x and in standard form with a leading coefficient of 1. ______

Identify root -1 factor: The factor for the root -1 is (x - (-1)) which simplifies to (x + 1).Identify root -6 factor: The factor for the root -6 is (x - (-6)) which simplifies to (x + 6).Multiply factors: Now we multiply the factors (x + 1) and (x + 6) to get the polynomial. (x + 1)(x + 6) = x^2 + 6x + x + 6Combine like terms: Combine like terms to write the polynomial in standard form. x^2 + 6x + x + 6 = x^2 + 7x + 6

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Write a polynomial of least degree with roots $-1$ and $-6$ . $\newline$ Write your answer using the variable $x$ and in standard form with a leading coefficient of $1$ . $\newline$ ______

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Precalculus

Write a polynomial from its roots

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Q. Write a polynomial of least degree with roots

-1

and

-6

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

______

Identify root $-1$ factor: The factor for the root $-1$ is $(x - (-1))$ which simplifies to $(x + 1)$ .
Identify root $-6$ factor: The factor for the root $-6$ is $(x - (-6))$ which simplifies to $(x + 6)$ .
Multiply factors: Now we multiply the factors $(x + 1)$ and $(x + 6)$ to get the polynomial. $(x + 1)(x + 6) = x^2 + 6x + x + 6$
Combine like terms: Combine like terms to write the polynomial in standard form. $\newline$ $x^2 + 6x + x + 6 = x^2 + 7x + 6$