Division of Polynomials
Remainder Theorem/Division
Factor Theorem
Multiplying Polynomials
Addition and Subtraction
100
Which of the following is equivalent to
x2 - 11x + 37 -128/(x+4)
A) (x3 +3x2-x-3)/(x+4) B) (x3-7x2-7x+20)/(x+4)
C)(x3-4x2+6x-4)/(x+4)
D) (3x3+17x2+21x-9)/(x+4)
B
100
Find the remainder when 8x3-66x2+14x+8 is divided by (x-8)
-8
100
x+4 is a factor of 4x3 -8x2 +12x+k . Find the value of k
432
100
If f(x) = 4(x + 3) and g(x) = 2(x2 – 3x + 2) Calculate the value of f(x). g(x)
8x3 - 56x + 48
100
Subtract 5x3 – 5x +12 from 8x3 – 12x + 8.
3x3 -7x -4
200
Express (x2 + x - 5)/(x2 + 5x + 3) in the form
q(x) + r(x)/a(x)
1 + (-4x-2)/(x2+5x+3 ) or 1 - (4x+2)/(x2+5x+3
200
The remainder when x2 +ax + 10 divided by (x - 1) is 4. Find the value of "a"
-7
200
p(x) = x3 -3x2 - 10x + k, has a factor of x+3. Which is another factor?
A) (x-3) B) (x-2) C) (x+2) D)(x+4)
B) x - 2
200
Simplify -3a2x5 (-2a3x3 - 9x3 + 2a).
6a5x8 + 27a2x8 - 6a3x5
200
If f(x) = 2(x + 3) and g(x) = 3(x2– 3x + 2) . Calculate the value of f(x) - g(x)
-3x2 + 11x
300
The function f(x) = x3 -7x2 + 2x + 40 has a zero at
x = 5. What are the other zeros of the function?
x= -2 and x= 4
300
The remainder when x4+11x3+ax2+24x+32 is divided by (x+6) is -4 . Find the value of "a"
a = 33
300
If (x-2) is a factor of x3 - x2 +ax - 2. Find the value of "a"
a = -1
300
If f(x) = 3(x + 3) and h(x) = (3x2–2x +3). Calculate the value of 
120
300
f(x) = 3x + 5 and g(x) = 2x - 1. Find an expression for f(x) + g(x)
5x + 4
400
The function f(x) , has (x-3) as one of the factors. Find the other two factors of f(x)
f(x) = x3 - x2 - 14x +24
(x-2) and (x+4)
400
Which expression is equivalent to
(6x2 + 7x)/(2x + 3) ?
A) 3x-1+ 3/(2x+3) B)3x+1 + 3/(2x+3)
C) 3x-1 + 3/(6x2+7x) D) 3x+1 +3/(6x2 +7x)
A
400
Given that (x-2) is a factor of the polynomial
x4 - 8x3 + 10x2 + bx + 4. Find the value of "b"
b = 2
400
Express 2(x-5)2 in standard form
2x2 - 20x + 50
400
f(x) = x3 - 2x2 and g(x) = 3x2 - 4x3 . Find an expression for f(x) - g(x)
5x3 - 5x2
500
What is x3 -1 divided by (x+3) ?
(x2 - 3x + 9) -28/(x+3)
500
(x2 - 3x - 21) divided by (x - 7 ) can be written in the form q(x) + r(x)/b(x) . Find an expression for the polynomial q(x)
x+4
500
Given that (x+2) is a factor of the polynomial
x4 + kx3 + 21x2 + 6x - 8
k = 10
500
A polynomial,p(x),has a lead coefficient of 1 and exactly three distinct zeros.
- x = 1 is a zero with multiplicity one
- x = 2 is a zero with multiplicity one
- x = -3 is a zero of multiplicity two . Find the equation of this polynomial in standard form.
x3 - 7x + 6
500
f(r) = (9r3 + 5r2 + 11r) and g(r) =(−2r3 + 9r − 8r2 )
7r3 − 3r2 + 20r