Question

if remainder of (5m+1)(5m+3)(5m+4)/5 is a natural number then find it

Answer 1

Answer:

2

Step-by-step explanation:

Easy way... Use congruences:

(5m+1)(5m+3)(5m+4) ≡ (1)(3)(4) = 12 ≡ 2 (mod 5)

Harder way...  Expand:

(5m+1)(5m+3)(5m+4)

= 5³m³ + 5²m²(1+3+4) + 5m((1)(3)+(1)(4)+(3)(4)) + (1)(3)(4)

= 5³m³ + 5²m²×8 + 5m×19 + 12

= 5 × ( 5²m³ + 5m²×8 + m×19 + 2 ) + 2

[ last step used 12 = 5 × 2 + 2 ]

So when (5m+1)(5m+3)(5m+4) is divided by 5, the remainder is 2.

Answer 2

Answer:

I have given you answer in the pic