Write a polynomial of least degree with roots 6 and -5. Write your answer using the variable x and in standard form with a leading coefficient of 1. ______

Write linear factors for root 6: To find a polynomial with given roots, we start by writing the linear factors associated with each root. For the root 6, the corresponding linear factor is (x - 6).Write linear factors for root -5: Similarly, for the root -5, the corresponding linear factor is (x + 5).Multiply linear factors: The polynomial of least degree with these roots is obtained by multiplying these linear factors together. So we multiply (x - 6) by (x + 5).Perform multiplication: Performing the multiplication, we get: (x - 6)(x + 5) = x^2 + 5x - 6x - 30.Simplify the expression: Simplify the expression by combining like terms: x^2 + 5x - 6x - 30 = x^2 - x - 30.

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Algebra 2

Write a polynomial from its roots

Full solution

Q. Write a polynomial of least degree with roots

6

and

-5

\newline

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

\newline

______

Write linear factors for root $6$ : To find a polynomial with given roots, we start by writing the linear factors associated with each root. For the root $6$ , the corresponding linear factor is $(x - 6)$ .
Write linear factors for root $-5$ : Similarly, for the root $-5$ , the corresponding linear factor is $(x + 5)$ .
Multiply linear factors: The polynomial of least degree with these roots is obtained by multiplying these linear factors together. So we multiply $(x - 6)$ by $(x + 5)$ .
Perform multiplication: Performing the multiplication, we get: $(x - 6)(x + 5) = x^2 + 5x - 6x - 30$ .
Simplify the expression: Simplify the expression by combining like terms: $x^2 + 5x - 6x - 30 = x^2 - x - 30$ .