WORKSHEET ON DIVIDING POLYNOMIALS FOR SAT

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

Solution

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)

Solution

Problem 3 :

x³ - 3x² + 3x - 9 = 0

For what real value of x is the equation above true?

Solution

Problem 4 :

What is the remainder when x² + 2x + 1 is divided by x + 3?

Solution

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?

Solution

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?

Solution

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

Solution

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

Solution