Determine the remainder of the following polynomial divisions using the remainder theorem
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A+ TUTORIAL FOR THE FOLLOWING QUESTIONS
Polynomial Functions
Polynomial Inequalities
Polynomial Functions Unit Assignment
1.Determine the remainder of the following polynomial divisions using the remainder theorem:
a.(4x4 + 3x2 - x + 3) (x + 1)
b.(3x2 + 2x - 7) (2x - 1)
(2 marks)
2.Complete the square to find the vertex of each quadratic function. State the vertex.
a.f(x) = x2 + 8x 3
b.f(x) = x2 5x + 8
c.f(x) = 2x2 12x + 1
d.f(x) = 3x2 + 2x 5
(10 marks)
3.Factor each of the following trinomials:
a.y2 + 3y 108
b.15s2 + 26s + 8
c.x4 5x2 36 (hint: let a = x2)
d.t2 + 4t 2
e.2w2 w 4
(14 marks)
4.If (x 3) divides evenly into x3 x2 kx + k, find k.
(2 marks)
5.If (x + 2) is a factor of m2x4 + 5mx3 + x2 7x 2, find m.
(4 marks)
6.When px3 2px2 + 3x p is divided by (x 1), the remainder is -5. Find p.
(2 marks)
7.Let f(x) = ax3 + bx2 + 3x 4. If f(x) is divided by (x 2), the remainder is 2. When it is divided by (x 1), the remainder is -2. Find a and b.
(4 marks)
8.Solve the following polynomial inequalities.
a.4x - 5 ? 2(x - 7
b.x3 - 5x2 + 2x ? -8
c.2(x3 - 2x2 + 3)