Polynomials Tes...

A triangular park with length of the first side (3x³ + 7x² - 8) m and length of the second side (5x³ - 9x² - 2) m has perimeter (12x³ - 8x² - 10) m. Find the length of the third side of the park.

In the first week, Priya spent Rs. (10x³ + 5x² + 2) for buying pencils. In the second week, she bought (9x² + 10) pencils and the price of each pencil was Rs. (2x + 4). How much did she spend altogether in two weeks?

If the weight of one basket is (2x³ – 8x² + x – 4) kg and the weight of another basket is (4x³ + 12x² + 2x + 6)kg, then what will be the biggest measure that can measure both quantities exactly?

On dividing x³ + 2x² - 4x + 7 by x + 2, the quotient and the remainder are x² - a and 15, respectively. What is the value of a?

Let R₁ and R₂ be the remainders when the polynomials x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by x + 1 and x - 2, respectively.

Which of the following is the value of a if 2R₁ + R₂ = 6?

If 2 and -2 are zeros of the polynomial Qx⁵ – Px⁴ + Zx³ + Rx² + M, find the values of the following:

(i) 8R + 2M
(ii) 4Q + Z