Problem 1 :
Without performing division, find the remainder when
x^{3} + 2x^{2 }- 7x + 5 is divided by x - 1
Problem 2 :
Without performing division, find the remainder when
x^{4} - 2x^{2} + 3x - 1 is divided by x + 2
Problem 3 :
Find a given that:
when x^{3} - 2x + a is divided by x - 2, the remainder is 7.
Problem 4 :
Find a given that:
when 2x^{3} + x^{2} + ax - 5 is divided by x + 1, the remainder is -8
Problem 5 :
Find a and b given that when x^{3} + 2x^{2} + ax + b is divided by x - 1 the remainder is 4, and when divided by x + 2 the remainder is 16.
Problem 6 :
2x^{n} + ax^{2} - 6 leaves a remainder of -7 when divided by x - 1, and 129 when divided by x + 3. Find a and n given that n∈Z^{+}.
Problem 7 :
When P(z) is divided by z^{2} - 3z + 2 the remainder is 4z - 7. Find the remainder when P(z) is divided by:
a. z - 1 b. z - 2
Problem 8 :
When P(z) is divided by z + 1 the remainder is -8 and when divided by z - 3 the remainder is 4. Find the remainder when P(z) is divided by (z - 3) (z + 1).
1) The remainder is 1.
2) The remainder is 1.
3) a = 3
4) The value of a is 2.
5) So, the values of a and b is -5 and 6.
6) The values of a and n is -3 and 4.
7) a) P(1) = -3 b) P(2) = 1
8) remainder is 3z - 5.
Use the remainder theorem to find f(k).
Problem 1 :
k = 2; f(x) = x² - 2x + 5
A) -5 B) -3 C) -13 D) 5
Problem 2 :
k = -3; f(x) = x² + 2x + 2
A) 1 B) -13 C) 5 D) -17
Problem 3 :
k = -2; f(x) = 3x³ - 7x² - 3x + 3
A) 14 B) -55 C) -43 D) -5
Problem 4 :
k = 4; f(x) = x³ - 2x² + 5x - 2
A) 54 B) 50 C) -78 D) -76
Problem 5 :
k = 2; f(x) = 9x^{4} + 10x³ + 6x² - 6x + 16
A) 360 B) 500 C) 252 D) 36
Problem 6 :
k = 5; f(x) = x³ - 3x² - 4x - 5
A) 35 B) 25 C) -225 D) -220
Problem 7 :
Using the remainder theorem find the remainders obtained when x^{3} + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of the two remainders is 1.
1) Remainder = 5
2) Remainder = 5
3) Remainder = -43
4) Remainder = 50
5) Remainder = 252
6) Remainder = 25
7) k = -2
Problem 1 :
Given that x − 2 is a factor of the polynomial
x^{3} − kx^{2} − 24x + 28
find k and the roots of this polynomial.
Problem 2 :
Find the quadratic whose roots are −1 and 1/3 nd whose value at x = 2 is 10.
Problem 3 :
Consider the polynomial p(x) = x^{3} − 4x^{2} + ax − 3.
(a) Find a if, when p(x) is divided by x + 1, the remainder is −12.
(b) Find all the factors of p(x).
Problem 4 :
Consider the polynomial
h(x) = 3x^{3} − kx^{2} − 6x + 8
(a) Given that x − 4 is a factor of h(x), find k and find the other factors of h(x).
Problem 5 :
Find the quadratic which has a remainder of −6 when divided by x − 1, a remainder of −4 when divided by x − 3 and no remainder when divided by x + 1
Problem 6 :
Find the value of a if x − 3 is a factor of f(x)= x^{3} - 11x + a
Problem 7 :
Find the value of k if f(x) = 3(x^{2} + 3x - 4) - 8(x - k) is divisible by x.
Problem 8 :
If x − 2 is a factor of polynomial
p(x) = a(x^{3} - 2x) + b(x^{2} - 5)
which of the following must be true ?
a) a + b = 0 b) 2a - b = 0 c) 2a + b = 0 d) 4a - b = 0
1) k = -2
2) p(x) = 2(x + 1) (x - 1/3)
3) (x + 1) and (x^{2} - 5x - 3) are factors.
4) k = 11
5) p(x) = x^{2} - 3x - 4
6) a = 6
7) k = 3/2
8) 4a - b = 0
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM