PRACTICE QUESTIONS ON OPERATION OF POLYNOMIALS FOR SAT

Problem 1 :

(3x + 2y)2

If the expression above can be written as ax2 + bxy + cy2, where a, b and c are constants, what is the value of a + b + c ?

Solution

Problem 2 :

Which of the following expression is not equivalent to

ab (c + d) ?

(a)  abd + abc     (b)  ab(d + c)     c(c)  ab (c + d)   (d) abc + bd

Solution

Problem 3 :

x2 + kx + 9 = (x + a)2

In the equation above, k and a are positive constants. If the equation is true for all values of x, what us the value of k ?

Solution

Problem 4 :

For all x ≠ 3, the expression above is equivalent to 

kx(x-3)2

where k is positive constant. What is the value of k ?

Solution

Problem 5 :

If  a = x2 - 5x + 2 and b = 3x3 + 4x2 - 6, what is 3a - b in terms of x ?

(a) 4x2 - 15x + 12      (b)  -3x3 - 4x2 - 15x + 12

(c) -3x3 - x2 - 15x      (d) -3x3 + 7x2 - 15x + 12

Solution

Problem 6 :

Based on the equation above, which of the following is possible value of (x - 2) ?

(a)  √3     (b)  -2 + √3     (c)  2 - √3   (d) 3

Solution

Problem 7 :

If a4 - b2 = 30 and a2 + b = -5, what is the value of a2 - b ?

(a)  -6   (b)  -2    (c) 3     (d)  6

Solution

Problem 8 :

If c = ab/d and d ≠ 0, then 1/ab = 

(a)  c + d   (b)  cd     (c) 1/cd    (d) c/d

Solution

Problem 9 :

2x (x - y) (x + y) 

Which of the following is equivalent to the expression above ?

(a) 4x3 - 2xy2    (b)  2x3 + 2xy2

(c)  2x3 - 2xy     (d)  2x3 - 4xy + 2xy2

Solution

Problem 10 :

If y8 = m and y9 = 2/3, what is the value of y in terms of m ?

(a)  2m/3   (b)  2/3m   (c) 3m/2   (D) 3/2m

Solution

Problem 11 :

b(2a + 3) (2 + 5a)

What is the value of the coefficient of the ab term when the expression above is explained and the like terms are combined ?

Solution

Problem 12 :

If (x + 3) (x - 3) = 91, what is the value of x2 ?

Solution

Problem 13 :

a(3 - a) + 2(a + 5)

Which of the following is equivalent to the expression above ?

(a) -a2 + 5a + 5     (b)  -a2 + 5a + 10

(c)  4a + 5        (d)  4a + 10

Solution

Problem 14 :

If y > 0 and 

(a)  -3/2   (b) -5/2   (c) 3/2   (d) 5/2

Solution

Answer Key

1)  a + b + c = 25

2)  option c

3) k = 6 , -6

4)  k = 19

5)  - 3x3 - x2 - 15x + 12

6)  2 ± √3

7)  (a2 - b) = -6

8)  d/c = 1/ab

9)  2x3 - 2xy2

10)  y = 2/3m

11)  b(10a2 + 19a + 6)

12)  x = ±10

13)   -a2 + 5a + 10

14)  The value of b is -3/2.

Problem 1 :

If 10xy - 3y + 6 = 41 + 2y, what is the value of 2xy - y ?

(a)  5   (b)  6   (c)  7   (d)  15

Solution

Problem 2 :

2a+3ba - b = 34, then ab

Solution

Problem 3 :

If a = 2x3y2 - 3x2y3  and b = -3x3y2 + 2x2y3, what is a + b in terms of x and y ?

Solution

Problem 4 :

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 ?

Solution

Problem 5 :

If (mx + c) (nx + 3) = 12x2 + 5x - 3 for all values of x, where m, n and c are constants, what is the value of m + n ?

(a)  7   (b)  8  (c)  12   (d)  13

Solution

Problem 6 :

(75x2 - 20) - 10(6 + 7x2)

The expression above can be written in the form a(x + b)(x - b), where a and b are positive constants. What is the value of a + b ?

Solution

Problem 7 :

3(2xy + xyz + yz) - (3xy + 5xyz - 2yz)

It is equal to ?

Solution

Problem 8 :

Which of the following is equivalent to (m + n + 1) (m + n - 1) ?

(a) m2 + 2mn + n2 - 1    (b) m2 - 2mn + n2 - 1 

(c)  m2 - n2 - 1        (d)  m2 + 2m + n2 + 2n - 1

Solution

Problem 9 :

If a = 2/3b and ax = 5/6b for b ≠ 0, what is the value of x ?

Solution

Answer Key

1)  2xy - y = 7

2)  a/b = -3

3)  a + b = -x3y2 - x2y3

4)  k = -4

5)  m + n = 7

6)  a + b = 9

7)  3xy - 2xyz + 5yz

8)   m2 + 2mn + n- 1

9) x = 5/4

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