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A polynomial function $h(x)$ with integer coefficients has a leading coefficient of $-1$ and a constant term of $7$ . According to the Rational Root Theorem, which of the following are possible roots of $h(x)$ ? $\newline$ Multi-select Choices: $\newline$ (A) $1$ $\newline$ (B) $7$ $\newline$ (C) $-7$ $\newline$ (D) $-1$

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Rational root theorem

Full solution

Q. A polynomial function

h(x)

with integer coefficients has a leading coefficient of

-1

and a constant term of

7

. According to the Rational Root Theorem, which of the following are possible roots of

h(x)

?

\newline

Multi-select Choices:

\newline

(A)

1

\newline

(B)

7

\newline

(C)

-7

\newline

(D)

-1

Rational Root Theorem: The Rational Root Theorem states that any rational root, in the form of $\frac{p}{q}$ (where $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient), must be a factor of the constant term when the leading coefficient is $1$ .
Leading Coefficient: Since the leading coefficient is $-1$ , the possible values for $q$ are $\pm 1$ . This simplifies the possible roots to just the factors of the constant term, which is $7$ .
Possible Roots: The factors of $7$ are $\pm1$ and $\pm7$ . So, the possible rational roots are $1$ , $-1$ , $7$ , and $-7$ .
Check Choices: Check the choices given: (A) $1$ , (B) $7$ , (C) $-7$ , (D) $-1$ . All of them are listed as possible roots.

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