The expression $4 x^{3} - b x^{2} + x - c$ leaves remainders 0 and 30 when divided by x+1 and 2x-3 respectively. Calculate the values of b and c hence, factorize the expression completely.

Q. The expression

2 x^{3} + b x^{2} - c x + d

leaves the same remainder, when divided by

x + 1

x - 2

2 x - 1

. Find

b

and

c

Q. A polynomial

f (x)

leaves remainder

15

when divided by

(x - 3)

and

(2 x + 1)

when divided by

(x - 1)^{2}

. When

f

is divided by

(x - 3) (x - 1)^{2},

the remainder is

Join BYJU'S Learning Program

If the expression (x2−x+c) when divided by (x+1) leaves remainder 3, then the value of c is

The correct option is D 1f(x)=x2−x+c,divisor=(x+1)Now, According to Remainder theorem, f(−1)=3 implies (−1)2−(−1)+c=3∴c=1

If the expression $(x^{2} - x + c)$ when divided by $(x + 1)$ leaves remainder $3$ , then the value of $c$ is

The correct option is D $1$
$f (x) = x^{2} - x + c, d i v i s o r = (x + 1)$
Now, According to Remainder theorem, $f (- 1) = 3$ implies $(- 1)^{2} - (- 1) + c = 3$
$∴ c = 1$