Question

which expression has the factor (h + 2)?
a. h² + 6h + 5
b. 2h² + h
c. 2h² - 4h
d. h² + h - 2

Explanation:

Step1: Use factor - theorem

According to the factor - theorem, if \(h + 2\) is a factor of a polynomial \(P(h)\), then \(P(-2)=0\).

Step2: Evaluate option A

Let \(P_A(h)=h^{2}+6h + 5\). Then \(P_A(-2)=(-2)^{2}+6\times(-2)+5=4-12 + 5=-3
eq0\).

Step3: Evaluate option B

Let \(P_B(h)=2h^{2}+h\). Then \(P_B(-2)=2\times(-2)^{2}+(-2)=2\times4-2 = 6
eq0\).

Step4: Evaluate option C

Let \(P_C(h)=2h^{2}-4h\). Then \(P_C(-2)=2\times(-2)^{2}-4\times(-2)=2\times4 + 8=16
eq0\).

Step5: Evaluate option D

Let \(P_D(h)=h^{2}+h - 2\). Then \(P_D(-2)=(-2)^{2}+(-2)-2=4-2-2 = 0\).

Answer:

D. \(h^{2}+h - 2\)