Question

Use the remainder theorem to find the remainder for each division. Is the divisor a factor of the polynomial?

1) ( 10x³ - x² + 8x + 29) ÷ ( x+ 2/5 )

Answer 1

x+2/5
according to remainder theorem
x = -2/5

10x³-x²+8x+29
=10(-2/5)³-(-2/5)²+8(-2/5)+29
=10×-8/125 -(4/25)-16/5+29
=-80/125 - 4/25 - 16/5 +29
= -16/25 -4/25 - 16/5 +29
= -16-4-80+725/25
= -100+725/25
= 625/25
=25

remainder is 25
R =25

according to factor theorem if a divisor g(x) is the factor of the polynomial p(x) then p(g) should be p(g) = 0 so
no the divisor is not factor of polynomial