SAT PRACTICE PROBLEMS ON SYNTHETIC AND POLYNOMIAL DIVISION

Problem 1 :

The expression 

is equal to which of the following ?

a) -2 (b) -8x - 2 + 4(c) 8x - 2 + 4 (d) 4 - 2x

Solution

Problem 2 :

If the expression

is written in the form 

what us Q in terms of x ?

(a)  3x - 1    (b) 3x + 1    (c)  6x2 + 3x + 1    (c)  6x2 + 5x + 1

Solution

Problem 3 :

The expression 4x2 + 5 can be written as A(2x - 1) + R, where A is an expression in terms of x and R is constant. What is the value of R?

Solution

Problem 4 :

synthetic-polynomial-divisionq4

The function g is defined by a polynomial. The table above shows some values of x and g(x). What is the remainder when g(x) is divided by x + 3 ?

(a)  -2    (b)  1    (c)  2    (d)  6

Solution

Problem 5 :

2z3 - kxz2 + 5xz + 2x - 2

In the polynomial above, k is constant. If z - 1 is a factor of the polynomial above, what is the value of k ?

Solution

Problem 6 :

When 3x2 - 8x - 4 is divided by 3x - 2, the result can be expresses as 

What is A in terms of x ?

(a)  x - 4     (b)  x - 2    (c) x + 2   (d) x + 4

Solution

Problem 7 :

The expression 2x2 - 4x - 3 can be written as A(x + 1) + B, where B is constant. What is A in terms of x ?

(a)  2x + 6     (b)  2x + 2    (c) 2x - 2    (d) 2x - 6

Solution

Problem 8 :

The expression x2 + 4x - 9 can be written as (ax + b)(x - 2) + c, where a, b and c are constants. What is the value of a + b + c ?

(a)  -2     (b)  3    (c) 7    (d) 10

Solution

Problem 9 :

For a polynomial p(x), p(2) = 0. Which of the following must be true about p(x) ?

(a) 2x is a factor of p(x)      (b)  2x - 2 is a factor of p(x)

(c)  x - 2 is a factor of p(x)     (d)  x + 2 is a factor of p(x)

Solution

Problem 10 :

If p(x) = x3 + x2 - 5x + 3, then p(x) is divisible by which of he following ?

I.  x - 2       II.  x - 1   III. x + 3

(a) I and II only        (b)  I and III only

(c)  II and III only       (d)  I, II and III

Solution

Problem 11 :

If the polynomial p(x) is divisible by x - 2, which of the following could be p(x)

(a) p(x) = -x2 + 5x - 14       (b) p(x) = x2 - 6x - 2 

(c)  p(x) = 2x2 + x - 8      (d)  p(x) = 3x2 - 2x - 8 

Solution

Problem 12 :

If x - 1 and x + 1 are both factors of the polynomial

ax4 + bx3 - 3x2 + 5x

and a and b are constants, what is the value of a ?

(a)  -3    (b)  1      (c) 3     (d)  5

Solution

Problem 13 :

For a polynomial p(x), p(1/3) = 0. Which of the following must be a factor of p(x)

(a)  3x - 1    (b)  3x + 1      (c) x - 3     (d)  x + 3

Solution

Answer Key

1)  option c

2)  3x + 1

3) 6

4)  2

5) k = 7

6)  x - 2

7) 2x - 6

8) a + b + c = 10

9)  Then x - 2 is a factor

10) So, I and III are factors.

11) 3x2 - 2x - 8

12)  3

13)  (3x - 1)

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