The correct option is A (x+1), (4x2–3x+8)
Let us assume that atleast one of the zeroes is an integer. Product of the factors is equal to the constant term (+8). Possible roots are the factors of +8. Hence, possible factors are:
±1,±2,±4,±8.
Trying -1, we get:
p(−1)=4×(−1)3+(−1)2+5×(−1)+8
p(−1)=−4+1−5+8=0
So, (x + 1) is a factor of the polynomial P(x).
The quotient obtained when p(x) is divided by (x + 1) is the other factor.
4x2−3x+8x+1 )¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 4x3+x2+5x+8 −4x3±4x2–––––––––––– −3x2+5x∓3x2∓3x–––––––––––– 8x+8−8x±8––––––––– 00
The factors are x+1 & 4x2−3x+8.