If x+7 is a factor of the polynomial function g, what is the value of g(7) ? Choose 1 answer: (A) -7 (B) 0 (C) 14 (D) Cannot be determined from the given information

Understand Relationship: Understand the relationship between factors of a polynomial and the value of the polynomial. If x+7 is a factor of the polynomial function g, then g(x) = 0 when x = -7. This is because a factor of a polynomial is a binomial that, when set to zero, gives a root of the polynomial.Apply Factor Theorem: Apply the Factor Theorem. The Factor Theorem states that if x+7 is a factor of g(x), then g(-7) = 0. However, we are interested in g(7), not g(-7).Evaluate g(7): Evaluate g(7). Since we know that x+7 is a factor of g(x), and we are asked for g(7), we can directly substitute x = 7 into the polynomial to find g(7). g(7) = 0 because x+7 being a factor implies that g(x) has a root at x = -7, not at x = 7. Therefore, the value of g(7) cannot be determined solely based on the information that x+7 is a factor.

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If
x+7 is a factor of the polynomial function
g, what is the value of
g(7) ?
Choose 1 answer:
(A) -7
(B) 0
(C) 14
(D) Cannot be determined from the given information

If $x+7$ is a factor of the polynomial function $g$ , what is the value of $g(7)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-7$ $\newline$ (B) $0$ $\newline$ (C) $14$ $\newline$ (D) Cannot be determined from the given information

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Math Problems

Algebra 2

Solve quadratic inequalities

Full solution

Q. If

x+7

is a factor of the polynomial function

g

, what is the value of

g(7)

\newline

Choose

1

answer:

\newline

(A)

-7

\newline

(B)

0

\newline

(C)

14

\newline

(D) Cannot be determined from the given information

Understand Relationship: Understand the relationship between factors of a polynomial and the value of the polynomial. $\newline$ If $x+7$ is a factor of the polynomial function $g$ , then $g(x) = 0$ when $x = -7$ . This is because a factor of a polynomial is a binomial that, when set to zero, gives a root of the polynomial.
Apply Factor Theorem: Apply the Factor Theorem. $\newline$ The Factor Theorem states that if $x+7$ is a factor of $g(x)$ , then $g(-7) = 0$ . However, we are interested in $g(7)$ , not $g(-7)$ .
Evaluate $g(7)$ : Evaluate $g(7)$ . $\newline$ Since we know that $x+7$ is a factor of $g(x)$ , and we are asked for $g(7)$ , we can directly substitute $x = 7$ into the polynomial to find $g(7)$ . $\newline$ $g(7) = 0$ because $x+7$ being a factor implies that $g(x)$ has a root at $g(7)$ $0$ , not at $x = 7$ . Therefore, the value of $g(7)$ cannot be determined solely based on the information that $x+7$ is a factor.