Statement1: The polynomial P(x)=4x3–3x2+5x–6 when divided by x–1 gives zero as the remainder.
Statement2: (x–1) is a factor of the polynomial P(x)=4x3–3x2+5x–6.
Both the statements are true and statement 2 is the correct explanation of statement 1.
According to factor theorem when a polynomial P(x) gives zero as the remainder when divided by (x – a), where ‘a’ is any real number, then (x – a) is the factor of the polynomial P(x).
For the given polynomial P(x)=4x3–3x2+5x–6
P(1)=4(1)3–3(1)2+5(1)–6=0
Since P(1)=0, (x-1) is a factor of P(x).
When P(x) is divided by (x-1), the remainder will be zero.
Thus, statement 2 is the correct explanation to statement 1.