Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A polynomial function $g(x)$ with integer coefficients has a leading coefficient of $-2$ and a constant term of $8$ . According to the Rational Root Theorem, which of the following are possible roots of $g(x)$ ? $\newline$ Multi-select Choices: $\newline$ (A) $-\frac{12}{7}$ $\newline$ (B) $\frac{11}{20}$ $\newline$ (C) $-\frac{5}{3}$ $\newline$ (D) $1$

View step-by-step help

View step-by-step help

Rational root theorem

Full solution

Q. A polynomial function

g(x)

with integer coefficients has a leading coefficient of

-2

and a constant term of

8

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

g(x)

?

\newline

Multi-select Choices:

\newline

(A)

-\frac{12}{7}

\newline

(B)

\frac{11}{20}

\newline

(C)

-\frac{5}{3}

\newline

(D)

1

Understand Rational Root Theorem: The Rational Root Theorem states that any rational root, in the form of $\frac{p}{q}$ (where $p$ and $q$ are integers), of the polynomial equation with integer coefficients must have $p$ as a factor of the constant term and $q$ as a factor of the leading coefficient.
Factors of Constant Term: List the factors of the constant term $8$ : $\pm1$ , $\pm2$ , $\pm4$ , $\pm8$ .
Factors of Leading Coefficient: List the factors of the leading coefficient $-2$ : $\pm 1$ , $\pm 2$ .
Generate Possible Rational Roots: Generate all possible rational roots by combining the factors of the constant term with the factors of the leading coefficient: $\pm\frac{1}{1}$ , $\pm\frac{2}{1}$ , $\pm\frac{4}{1}$ , $\pm\frac{8}{1}$ , $\pm\frac{1}{2}$ , $\pm\frac{2}{2}$ , $\pm\frac{4}{2}$ , $\pm\frac{8}{2}$ .
Simplify List of Roots: Simplify the list of possible rational roots: $\pm 1$ , $\pm 2$ , $\pm 4$ , $\pm 8$ , $\pm \frac{1}{2}$ , $\pm \frac{4}{2}$ .
Check Options Against List: Further simplify the list by removing duplicates and unnecessary fractions: $\pm1$ , $\pm2$ , $\pm4$ , $\pm8$ , $\pm\frac{1}{2}$ .
Check Options Against List: Further simplify the list by removing duplicates and unnecessary fractions: $\pm 1$ , $\pm 2$ , $\pm 4$ , $\pm 8$ , $\pm \frac{1}{2}$ .Check each option against the list of possible rational roots: $\newline$ (A) $-\frac{12}{7}$ is not in the list, so it's not a possible root. $\newline$ (B) $\frac{11}{20}$ is not in the list, so it's not a possible root. $\newline$ (C) $-\frac{5}{3}$ is not in the list, so it's not a possible root. $\newline$ (D) $1$ is in the list, so it is a possible root.

More problems from Rational root theorem

Question

Find the degree of this polynomial.

\newline

`5b^{10} + 3b^3`

\newline

Posted 2 months ago

Question

\newline

(9a + 5) - (2a + 4)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3v^2(v^2 - 9)

\newline

Posted 1 month ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 2 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 2 months ago

Question

Divide. If there is a remainder, include it as a simplified fraction.

\newline

(24t^2 + 36t) \div 6t

\newline

Posted 2 months ago

Question

Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

\newline

\text{[[even][odd][neither]]}

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3q^2(-3q^2 + q)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 2 months ago

Question

Find the roots of the factored polynomial.

\newline

(x + 7)(x + 4)

\newline

Write your answer as a list of values separated by commas.

\newline

x =

Posted 2 months ago