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 

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 - 2xy²      (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

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 :

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