OPERATIONS WITH POLYNOMIALS SAT PRACTICE QUESTIONS

Problem 1 :

Which of the following gives the solution set for the polynomial equation below?

𝑥² − 11𝑥 + 19 = −5

A) {-3, -8}     B) {3, 8}     C) {-3, 8}      D) {3, -8}

Solution

Problem 2 :

Which of the following is a solution for the equation below?

7𝑟² − 14𝑟 = −7

A) -1     B) 0     C) 1       D) 7

Solution

Problem 3 :

Which of the following is equivalent to the expression above?

Solution

Problem 4 :

If x > 3, which expression is equivalent to

Solution

Problem 5 :

If

(ax + 2)(bx + 7) = 15x² + cx + 14

for all values of x, and a+b = 8, what are the two possible values for c ?

A) 3 and 5        B) 6 and 35       C) 10 and 21      D) 31 and 41

Solution

Problem 6 :

If t > 0 and t² - 4 = 0, what is the value of t ?

Solution

Problem 7 :

h(t) = −4.9t² + 25t

The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?

A) 3.5      B) 4.0      C) 4.5      D) 5.0

Solution

Problem 8 :

For a polynomial p(x), the value of p(3) is −2. Which of the following must be true about p(x ) ?

A) x − 5 is a factor of p (x)         B) x − 2 is a factor of p(x)

C) x + 2 is a factor of p(x)

D) The remainder when p(x) is divided by x − 3 is −2.

Solution

Problem 9 :

For what value of x is the function h above undefined?

Solution

Problem 10 :

x² - 34x + c = 0

In the given equation, c is a constant. The equation has no real solutions if c > n . What is the least possible value of n?

Solution