Polynomials Tes...

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?

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'.

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).