Polynomials Tes...

The value of m for which (x + 3) is a factor of (x + 2)⁶ – (3x + m)⁴ is ____.

The remainder obtained when x⁶ - y⁶ is divided by x + y is _____.

When p(x) = x ³- ax² + 3x – a is divided by (x – a), the remainder obtained is _____.

x¹⁸ – y¹⁸ can also be written as

If m = , n = , o = , then the value of is ______.

If (x + 3) and (x + 4) are the factors of (2x³+ 5x² + ax + b), then find the values of a and b.

x = 3 is a solution of x³+ 2x² – 9x – 18 = 0. What is/are the other solution(s)?

If (x + m) is a common factor of f(x) = (x² - ax - b) and g(x) = (x²+ px - q), then m is equal to

The product of polynomials [(x + y)² - 2xy] and (x⁴ + y⁴ – x²y²) is equal to __________.

If (x - m)³ + (x - n)³ + (x - o)³ = 3(x - m) (x - n) (x - o), then what is the value of 3x - m - n - o?

If , then what is the value of R?

When x³ - 3x² + gx - h is divided by x² - x - 12, the remainder obtained is 0. What is the value of ?

What will be the remainder obtained when the expression x³ + 7x² + 14x + 14 is divided by x + 4?

Which of the following is true if x² - 25 is a factor of px⁴ + qx³ + rx² + sx + t?

If and a + b + c = 3, then find the value of a² + b² + c².

There are (3a + 4b) biscuits in a pack and (4b - 3a) packs in a box. Now, if there are 16b² + 9a² boxes in a store, then find the total number of biscuits in the store.

The area of a triangular garden is (3x² + 2.5x - 3) m². Which among the following can be a possible combination of height and base of the triangle?

Devinder had x³ - 2x² - 12x + 16 candies. He distributed them equally among (x – 4) friends. If he gave each friend the maximum possible number of candies while dividing equally among them, then find the number of leftover candies.

Side of an equilateral triangle ism. Length and width of a rectangle are (x² + 4) and (x² - 4). Find the sum of the areas of the equilateral triangle and the rectangle.

Kavya has (x³ + x² - 2ax - 2b) sweets. In order for no sweets to be left over, she can equally share them among either (x – 2) children or (x + 1) children. If x = 5, then find the number of sweets she has.

Which of the following statements is INCORRECT?

If (4x² + 6x + 1)² – (3x² + 2x + 3)² is divided by (x² + x + 1), then what will be the quotient and the remainder obtained, respectively?

Select the correct statement(s):

(A) If x =, then the value ofis.
(B) Every rational number terminates as a decimal expansion.
(C) There are five real numbers between -3 and 2.
(D) When x² - 3x + 5 is divided by x - 2, the remainder obtained is 0.

Match the following:

Column - I	Column - II
(p) If f(x) = x3+ 25x2+ 9x – 16, then f(3) =	(I) 263
(q) If f(x) = 2x3+ 3x2+ 19x – 25, then f(-1) =	(II) -43
(r) If x = is a root of f(x) = 10x3- 5x2+ ax - 12, then a =	(III)
(s) If x = 1 is a root of f(x) = x152+ 2x87– m, then m =	(IV) 3

Study the given equations:

Equation I:

Equation II: