Polynomials Tes...

What is the value of 'a' for which (z + 2) is a factor of the polynomial -2z⁴ - 7z³ - 3z² - az - 10?

a⁸ - b⁸ equals

What is the remainder when a³ - b³ is divided by (a - b)?

If a = , b = and c = , then the value of is

What is the remainder when p(y) = y³ + ay² - 2y + a is divided by (y + a)?

If 3x³ - ax² - 2bx - 7 leaves a remainder of 5 when divided by (x - 2), then which of the following is the value of a + b?

What is the value of x + y if (a + 1) and (a + 2) are the factors of p(a) = xa³ + a² - 2a + y?

Let x and y be real numbers such that (x² – y²)(x² – 2xy + y²) = 3 and x – y = 1. What is the value of xy?

What will be value of 'l' if (x - l) is a common factor of f(x) = x² + ax + b and g(x) = x² + cx + d?

What will be the value of (a² + 9b²) (a + 3b) (a - 3b)?

If 4t³ - at² + 7 and t² + at + 8 leave the same remainder when divided by (t - 1), then what is the value of a?

What is the value of k if = (x - 1) + ?

Find the remainder when the expression 2x³ + 3x² - 14x – 20 is divided by (x – 4).

Find the value of k if (x + 2) is a factor of .

The length, breadth and height of a cuboidal tank are (2p + q) cm, (2p – q) cm, and (4p²+ q²) cm, respectively. Find the volume of the tank.

The length and breadth of a rectangle are (4x + 3) m and (2x – 5) m, respectively. What will be the area of the rectangle?

What must be added to x⁴ + 2x³ – 2x² + x – 1, so that the result is exactly divisible by x² + 2x – 3?

^{A farmer has to pack x3 - 4x2 + 2x + 5 apples in trays. Each tray can hold (x – 2) apples. How many apples would remain in the end after filling the trays?}

Rahul has Rs. (x³ + 5x² + px + q). With this money he can buy exactly (x - 2) balls or (x + 2) gloves with no money left. What would be the value of 'q'?

If the polynomial x³ - px² - 4x + 12 leaves the same remainder on dividing by (x - 3) and (x - 2), find the value of 'p'.

R₁ and R₂ are remainders when x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by (x + 1) and (x) - 1, respectively. If 2R₁ + R₂ = 6, find the value of a.

PART (i) REJECTED

Which of the following statements is/are correct?

(i) If y = , then the value of y² - 4y + 1 is 0.

(ii) The degree of the zero polynomial is zero.

(iii) If m² + n² + 2m + 1 = 0, then the value of m³¹ + n³⁵ is 1.

PART (A) REJECTED

Match the following:

Column - I	Column - II
(A) If f(x) = , then the value of f(-3) is	(i) 0
(B) If h(x) = , then equals	(ii) -110
(C) If p(x) = x201 + 5, then {p(8) + p(-8)} is equal to	(iii) 1
(D) is a polynomial of degree	(iv) -10

If , find the value of ^.

Directions: Consider the two statements and choose the correct option accordingly.

Statement 1: If (x + 6) and (x – 4) are factors of the expression 2x³+ 2ax² + 2bx – 24, then the value of 'b' is -23.
Statement 2: One of the factors of the expression (2x³– 134x + 252) is (2x - 14). On factorising the expression, the other two factors are (x – 2) and (x + 9).