POLYNOMIAL FUNCTIONS AND THEIR GRAPHS SAT WORKSHEET

Problem 1 :

If -1 and 1 are two real roots of the polynomial function 

f(x) = ax³ + bx² + cx + d

and (0, 3) is the y-intercept of graph f, what is the value of b ?

a)  -3    b)  -1    c)  2      d)  4

Solution

Problem 2 :

What is the remainder of the polynomial

p(x) = 81x⁵ - 121x³ - 36

is divided by x + 1 ?

Solution

Problem 3 :

If x - 2 is a factor of polynomial

p(x) = a(x³ - 2x) + b(x² - 5)

Which of the following must be true ?

a) a + b = 0    b)  2a - b = 0    c)  2a + b = 0   d)  4a - b = 0

Solution

Problem 4 :

The function f is defined of the polynomial. Some values of x and f(x) are shown in the table above. Which of the following must be a factor of f(x) ?

Solution

Problem 5 :

x³ - 8x² + 3x - 24 = 0

For what real of x is the equation above true ?

Solution

Problem 6 :

If x > 0, what is the solution of the equation

x⁴ - 8x² = 9 ?

Solution

Problem 7 :

If the graph of

f(x) = 2x³ + bx² + 4x - 4

intersects the x-axis at (1/2, 0) and (-2, k) lies on the graph of f. What is the value of k ?

a)  -4     b)  -2      c)  0       d)  2

Solution

Problem 8 :

The function y = f(x) is graphed on the xy- plane above. If k is a constant such that the equation f(x) = k has one real solution, which of the following could be the value of k?

a)  -3      b)  -1     c)  1      d)  3

Solution