Question

Using factor theorem, show that (2x+1) is a factor of 2x^3 + 3x^2 -11x - 6

Answer 1

Now, 2x+1=0
⇒x=-1/2
f(x)=2x³+3x²-11x-6
⇒f(-1/2)=2(-1/2)³+3(-1/2)²-11(-1/2)-6
             =2(-1/8)+3(1/4)+(11/2)-6
             =(-1/4)+(3/4)+(11/2)-6
             =(-1+3+22-24)÷4
             =0/4
             =0
∴(2x+1) is a factor of 2x³+3x²-11x-6