Problem 1:
The equation
is true for all values of x ≠ 2/3, where k is a constant. What is the value of k?
a.8 b.9 c.11 d.15
Problem 2 :
The expression
(3x² + 4) / (x + 1)
is equivalent to which of the following?
a. (3x - 3) + 1 / (x + 1) b. (3x - 3) + 7 / (x + 1)
c. (3x + 3) + 1 / (x + 1) d. (3x + 3) + 7 / (x + 1)
Problem 3 :
x³ - 3x² + 3x - 9 = 0
For what real value of x is the equation above true?
Problem 4 :
What is the remainder when x² + 2x + 1 is divided by x + 3?
Problem 5 :
When 3x² + x + 2 is divided by x - 1, the result can be expresses as
(ax + b) + c/(x - 1)
where a, b and c are constants. What is the value of a + b + c?
Problem 6 :
When 2x² - 5x + 3 is divided by 2x + 1, the result can be written as (x - 3) + R / (2x + 1), where R is a constant. What is the value of R?
Problem 7:
p(x) = (3x² - 5) (x + k) - 20
In the polynomial p(x) defined above, k is a constant. If x is a factor of p(x), what is the value of k?
a.-6 b.-4 c.2 d.4
Problem 8:
In the xy-plane, how many times does the graph of
f(x) = (x - 3) (x - 1) (x + 2)²
intersect the x-axis?
a.2 b.3 c.4 d.5
1) k is 15, option (d)
2) (3x - 3) + 7/(x + 1), option (b)
3) x = 3
4) p(-3) = 4
5) a + b + c = 13
6) R is 6.
7) k = -4, option b
8) The curve is intersecting the graph 3 times with multiplicity of -2 as 2, option b.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM