Question

If (3x−2) is a factor of the polynomial function g, write an equation for g as the product of linear factors.

A) g(x)=(x−3)(3x+2)(x−7)
B) g(x)=(3x−2)(x+6)(x−7)
C) g(x)=(x+3)(3x−2)(x−6)
D) g(x)=(x−3)(3x−2)(x+7)

Answer 1

To write the equation for the polynomial function g as the product of linear factors including (3x−2), the correct equation is B) g(x)=(3x−2)(x+6)(x−7), since it contains the specified factor.

Step-by-step explanation:

If (3x−2) is a factor of the polynomial function g, then to write an equation for g as the product of linear factors, you must ensure that (3x−2) is one of the factors in the equation. The options available are:

• A) g(x)=(x−3)(3x+2)(x−7)
• B) g(x)=(3x−2)(x+6)(x−7)
• C) g(x)=(x+3)(3x−2)(x−6)
• D) g(x)=(x−3)(3x−2)(x+7)

The correct answer is the one that includes (3x−2) as a factor. Looking at the options, the correct equation is B) g(x)=(3x−2)(x+6)(x−7), since it includes the required factor (3x−2). The other equations do not have the correct factor and therefore cannot be the equation for g if (3x−2) is indeed a factor.