which statement about -2h² - 15h - 7 is true? one of the factors is (h + 2). one of the factors is (3h - 2)…

Explanation:

Step1: Use the factor - theorem

The factor - theorem states that if (f(x)) is a polynomial and (f(a)=0), then ((x - a)) is a factor of (f(x)). Let (f(h)=-2h^{2}-15h - 7).

Step2: Test each option

Test ((h + 2)):

Set (h=-2) in (f(h)). Then (f(-2)=-2(-2)^{2}-15(-2)-7=-2\times4 + 30-7=-8 + 30-7=15\neq0), so ((h + 2)) is not a factor.

Test ((3h - 2)):

Set (h=\frac{2}{3}) in (f(h)). (f(\frac{2}{3})=-2(\frac{2}{3})^{2}-15\times\frac{2}{3}-7=-2\times\frac{4}{9}-10 - 7=-\frac{8}{9}-17=-\frac{8 + 153}{9}=-\frac{161}{9}\neq0), so ((3h - 2)) is not a factor.

Test ((2h+1)):

Set (h =-\frac{1}{2}) in (f(h)). (f(-\frac{1}{2})=-2(-\frac{1}{2})^{2}-15(-\frac{1}{2})-7=-2\times\frac{1}{4}+\frac{15}{2}-7=-\frac{1}{2}+\frac{15}{2}-7=\frac{-1 + 15}{2}-7=7 - 7=0). Since (f(-\frac{1}{2}) = 0), by the factor - theorem, ((2h + 1)) is a factor of (-2h^{2}-15h - 7).

Test ((h - 7)):

Set (h = 7) in (f(h)). (f(7)=-2\times7^{2}-15\times7-7=-2\times49-105 - 7=-98-105 - 7=-210\neq0), so ((h - 7)) is not a factor.

Answer:

One of the factors is ((2h + 1)).