Question

Find the value of 'a' if (x-2) is factor of 2x³ − 6x² + 5x + a.

Answer 1

Let p(x)=2x³ − 6x² + 5x + a and
and g(x)=x−2
x−2=0
x=2
If g(x) is a factor of p(x), then p(2) should be equal to zero.
p(2) = 2(2)³−6(2)²+5(2) + a = 0
16 – 24 + 10 + a = 0
2 + a = 0
a = -2