Remainder Theorem

Q. What is the remainder when 2^33 is divided by 17?

Q. What must be subtracted from $x^2-7x+19$ so that $x-3$ is a factor.

1. 7
2. -7
3. 8
4. -8

Q. Can (x − 2) be the remainder on division of a polynomial p(x) by (2x + 3)? Justify your answer.

Q. If the polynomial4x^4+2x^3-2x^2+x-1 Is divided by another polynomial x^2+2x-3 the remainder comes out to be ax+b then the values of a and b are

Q.

What is the remainder when x^1999 is divided by (x^2)-1?

Q.

When the polynomial $x^3+2x^2-5ax-7$ is divided by $(x-1)$, the remainder is A and when the polynomial $x^3+a{x}^2-12x+16$ is divided by $(x+2)$, the remainder is B. Find the value of 'a' if $2A+B=0$.

Q. If fourth degree polynomial is divided by a quadratic polynomial, write the degree of the remainder.

Q. Using division algorithm, find the quotient and remainder on dividing f(x) by g(x) where $f\left(x\right)=6x^3+13x^2+x-2andg\left(x\right)=2x+1.$

Q. Can ( x - 7 ) be the remainder on division of a polynomial p ( x ) by (7x+2) ? Justify your answer.

Q.

When divided by x-3 the polynomials x³-px²+x+6 and 2x³-x²-(p+3)x-6 leave the same remainder .Find the value of 'p'.

Q. Q. If polynomial x⁴-8x³-10x²+24x-10 is divided by x²+2x+k , the remainder comes out to be 64x+a , then find the values of k and a.

Q. Can (x-3) be the remainder on the division of a polynomial polynomial p(x) by (2x+5)?justify your answer.

Q. consider a polynomial f(x)=ax^2+bx+c such that f(0)=4 when f(x) is divided by x+1, we get remainder as 4 and when it is divided by x+2, we get remainder as 6. find the values of a, b, c.

Q.

The expression $4x^3-b{x}^2+x-c$ 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. If $x^{100}+2x^{99}+k$ is divisible by $(x+1)$, then the value of $k$ is:

1. 1
2. -3
3. 3
4. -2

Q.

When the polynomial f(x) = 4x³ + 8x² + 8x + 7 is divided by the polynomial g(x) = 2x² - x + 1, the quotient and the remainder are

1. Quotient = 2x - 5, Remainder = 11x

2. Quotient = x -5, Remainder = 13

3. Quotient = 2x + 5, Remainder = 11x + 2

4. Quotient = x² - 5, Remainder = 15

Q. On dividing $2x^2+3x+1$ by a linear polynomial g(x), the quotient is 2x – 1 and remainder is ‘r’, where $rϵR$, then g(x) is

1. x – 1
2. x + 1
3. x + 2
4. x + 4

Q. Find the quotient and remainder when
$f\left(x\right)=x^4-5x+6$ is divided by $g\left(x\right)=2-x^2$

Q.

Find in each case, the remainder when
(i) $x^4-3x^2+2x+1$ is divided by x - 1
(ii) $x^3+3x^2-12x+4isdividedbyx-2$
(iii) $x^4+1isdividedbyx+1.$

Q. Can y +5 be the remainder on the division of a polynomial f(y) by y​​​​​​ -2?

Q. Find the quotient and the remainder when:
$f\left(x\right)=x^3-3x^2+5x-3$ is divided by $g\left(x\right)=x^2-2$

Q. When the polynomial 2x^3+ 3X^2+ 3x-a is divided by x^2-1 , the remainder is 5x+b , then the value of (a+b) is

Q.

Factor Theorem is equivalent to Remainder Theorem when remainder is

1. 2
2. 4
3. 1
4. 0

Q.

Use the Remainder Theorem to find which of the following is a factor of $2x^3+3x^2-5x-6$
(a) x+1 (ii) 2x-1 (iii) x+2

Q.

Can (x-7) be the remainder on division of polynomial p(x)by (7x+2). Justify your answer

Q. 2x²-7x=39

Q. Why we write ax+b in place of r(x) when we have to find remainder in p(x)=[(x-α)(x-β]q(x)+r(x)

Q.

What number should be added to 3x² + 7x so that when the resulting polynomial is divided by x – 3 the remainder is 2?

1. -46

2. -30

3. -51

4. -25

Q.

48x^2-13x-1=0 by using squaring method

Q.

2x³+bx²-cx+d leaves the same remainder, when divided by x+1 (or)x-2(or)2x-1. Find b and c.