Lesson 8 - Remainder and Factor theorem
MULTIPLE CHOICE QUESTIONS
1. Find the remainder when x3 + 3x2 - 12x + 4 is divided by x – 2.
a) 1 b) 0 c) 3 d) 5
2. If (x - 2) is a factor of 2x3 – x2 – px – 2, find the value of p.
a) 5.1 b) 5 c) 6 d)7
3. Find the values of a and b when x – 2 and x – 3 both are factors of the
expression x3 + ax2 + bx -12.
a) 3,4 b) -3,4 c) -3,-4 d) 3,-4
4. The polynomials 3x3 – ax2 + 5x – 13 and (a + 1)x2 – 7x +5 leave the same
remainder when divided by x – 3. Find the value of ‘a’.
a) 5 b)4 c)9 d)6
5. x – 1 is a factor of x6 – x5 + x3 – x2 – x + 1.
a) True b) False
6. According to remainder theorem, if f(x), a polynomial in x, is divided by (x-a),
the remainder is:
a) f(a) b) f(x) c) f(-a) d)f
7. When f(x) = x3 + ax2 – bx – 8 is divided by x – 2, the remainder is zero and
when divided by x+1, the remainder is -30.Find the values of ‘a’ and ‘b’.
a) -7,-14 b) -8, -14 c) 7,-14 d) 7,14
8. What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting
expression has 2x+1 as a factor?
a) 0 b) 1 c) 2 d) 3
9. When a polynomial f(x) is divided by x – a and the remainder is 0, then x – a
is a remainder of polynomial f(x).
a) True b) False
10. Find the value of ‘k’ if (x – 2) if a factor of x3 + 2x2 – kx + 10.Determine
whether x+5 is also a factor.
a) 13, Yes b) -13, Yes c) 13, No d) 14, Yes
11. Find the remainder when x2 – 8x + 4 is divided by 2x + 1.
a) 8 ¼ b) 8 ½ c) 8.5 d) 8 ¾
12. When the polynomial 2x3 – kx2 + (5k – 3) – 8 is divided by x – 2 , the
remainder is 14. Find the value of ‘k’.
a) 3 b) 1 c) 2 d) 0
13. What number should be added to 2x3 – 3x2 + x so that when the resulting
polynomial is divided by x – 2 , the remainder is 3?
a) 3 b) -3 c) 2 d) 4
14. Polynomial x3 – ax2 + bx – 6 leaves a remainder -8 when divided by x – 1
and x – 2 is a factor of it. Find the values of ‘a’ and ‘b’.
a) -2.-5 b) 2,-5 c) -2, 5 d) 3,-5
15. 2x + 7 is a factor of 2x3 + 5x2 – 11x -14. Factorise the given expression
using the factor theorem.
a) (2x - 7)(x– 2)(x + 1) b) (2x + 7)(x – 2)(x + 1) c) (2x + 7)(x – 2)(x - 1)
d) (2x + 7)(x – 2)(x + 2)
16. Find the values of ‘a’ and ‘b’ so that the polynomial x3 + ax2 + bx – 45 has
(x – 1) and (x + 5) as its factors.
a) 13,31 b) 53, 31 c) 12,31 d) 31,13
17. Factorise using the remainder theorem: 4x3 + 7x2 – 36x – 63.
a) (x + 3)(x+3) b) (x + 3)(x – 3)(4x + 7) c) (x + 3)(x – 3)(4x – 7) d) None of
these
18. The polynomial px3 + 4x2 – 3x + q is completely divisible by x2 – 1; find the
values of p and q.
a) 3,-4 b) 3,4 c) 2,-3 d) -3,-4
19. Using Remainder Theorem, factorise: x3 + 3x2 – mx + 26.
a) (x + 3)(x – 3)(4x + 7) b) (x + 3)(x + 3)(4x + 7) c) (x + 3)(x – 3)(4x – 6)
d) (x – 1)(x – 2)(x+13)
20. Find the value of ‘a’ if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a
remainder of 5.
a) 2 b) 1 c) 4 d) 0
Answer Key:
1.b) 2.b) 3.d) 4.a) 5.b) 6.a) 7.a) 8.b) 9.b) 10.a)
11.a) 12.c) 13.b) 14.a) 15.b) 16.d) 17.b) 18.a) 19.d) 20.a)
