Polynomials Quiz

Find the square root of (x2 - 8x + 15)(2x2 - 11x + 5)(2x2 - 7x + 3).

1. (2x - 1)2(x - 3)(x - 5)
2. (2x - 1)(x - 5)(x - 2)(x - 3)
3. (2x - 1)(x - 5)(x - 3)
4. (x - 3)2(x - 5)(2x - 1)

Answer: (c) (2x - 1)(x - 5)(x - 3)

What is the value of √(x + y - 2√(xy)) when √x > √y?

1. √(xy)
2. √x + √y
3. √y - √x
4. √x - √y

Answer: (d) √x - √y

If the sum and difference of two expressions are 10x2 - 2x - 8 and 2x2 + 18x - 20, then what is their LCM?

1. (x + 1)(2x - 3)(3x + 7)
2. 2(x - 1)(2x - 3)(3x - 7)
3. 2(x - 1)(2x - 3)(3x + 7)
4. (x - 1)(2x - 3)(3x + 7)

Answer: (c) 2(x - 1)(2x - 3)(3x + 7)

Find the quadratic polynomial when divided by x, x - 1 and x - 2 leaving remainders 1, 2 and 9 respectively.

1. 2x2 - 3x + 1
2. 3x2 - 2x + 1
3. 6x2 - 5x + 3
4. 6x2 + 5x + 3

Answer: (b) 3x2 - 2x + 1

Find the factor of (x - b)5 + (b − a)5.

1. (x + a)
2. (a - b)
3. (x - b)
4. (x - a)

Answer: (d) (x - a)

Find the square root of 4x6 − 12x5 + 9x4 + 8x3 − 12x2 + 4.

1. 2x3 - 3x2 + 2
2. 6x3 - x2 + 1
3. 7x3 - 3x2 + 2
4. 2x3 - 3x2 + 4

Answer: (a) 2x3 - 3x2 + 2

If 4x2 - 6x + m is divisible by x - 3, which one of the following is greatest divisor of m?

1. -20
2. -18
3. -12
4. -15

Answer: (b) -18

If 1/(y + z) + 1/(z + x) = 2/(x + y), then what is the value of (x2 + y2) ?

1. 3z2
2. 2z2
3. 5z
4. 6z

Answer: (b) 2z2

Consider the equation p(x): ax² + bx + c = 0 whose coefficients a, b and c are all non-zero, and each of them satisfies an equation that results from removing the term containing that coefficent from the equation p(x); for example, the coefficient b is a solution of the equation ax² + c = 0. What is the sum of all solutions of p(x)?

1. always (- 1)
2. always 1
3. 1 or 2
4. 1 and -1

Answer: (d) 1 and -1

If (x + k) is a common factor of x2 + px + q and x2 + lx + m , then what is the value of k?

1. (q - m)/(p - l)
2. (q + m)/(p + l)
3. (q + m)(-p + l)
4. (q - m)(p - l)

Answer: (a) (q - m)/(p - l)