A third degree polynomial function y=g(x) is defined so that g((2)/(3))=0 and g(0)=5. Which of the following must be a factor of g ? Choose 1 answer: (A) x-5 (B) x+5 (c) 3x-2 (D) 3x+2

Given information: We are given that g((2)/(3))=0. This means that when x equals (2)/(3), the polynomial function g(x) equals zero. This implies that x minus (2)/(3) is a root of the polynomial, and therefore (x - (2)/(3)) must be a factor of g(x).Finding the factor: To express the factor with integer coefficients, we can multiply the factor (x - (2)/(3)) by 3 to clear the fraction. This gives us 3(x - (2)/(3)) = 3x - 2. Therefore, (3x - 2) must be a factor of g(x).Matching the factor: Now we look at the answer choices to see which one matches the factor we found. The factor we found is (3x - 2), which corresponds to answer choice (C).

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A third degree polynomial function
y=g(x) is defined so that
g((2)/(3))=0 and
g(0)=5. Which of the following must be a factor of
g ?
Choose 1 answer:
(A)
x-5
(B)
x+5
(c)
3x-2
(D)
3x+2

A third degree polynomial function $y=g(x)$ is defined so that $g\left(\frac{2}{3}\right)=0$ and $g(0)=5$ . Which of the following must be a factor of $g$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $x-5$ $\newline$ (B) $x+5$ $\newline$ (C) $3 x-2$ $\newline$ (D) $3 x+2$

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Math Problems

Algebra 1

Transformations of absolute value functions: translations and reflections

Full solution

Q. A third degree polynomial function

y=g(x)

is defined so that

g\left(\frac{2}{3}\right)=0

and

g(0)=5

. Which of the following must be a factor of

g

\newline

Choose

1

answer:

\newline

(A)

x-5

\newline

(B)

x+5

\newline

(C)

3 x-2

\newline

(D)

3 x+2

Given information: We are given that $g\left(\frac{2}{3}\right)=0$ . This means that when $x$ equals $\frac{2}{3}$ , the polynomial function $g(x)$ equals zero. This implies that $x - \frac{2}{3}$ is a root of the polynomial, and therefore $(x - \frac{2}{3})$ must be a factor of $g(x)$ .
Finding the factor: To express the factor with integer coefficients, we can multiply the factor $x - \frac{2}{3}$ by $3$ to clear the fraction. This gives us $3(x - \frac{2}{3}) = 3x - 2$ . Therefore, $(3x - 2)$ must be a factor of $g(x)$ .
Matching the factor: Now we look at the answer choices to see which one matches the factor we found. The factor we found is $(3x - 2)$ , which corresponds to answer choice $(C)$ .