factors and remainders in polynomial equation || Quantitative Aptitude || CAT 2021 || 18 May

The polynomial P (x) = x⁴ – 2x³ + 3x² – ax + 3a – 7 when divided by (x + 1) leaves the remainder 19. The value of a is

What is the remainder when the polynomial 2x³ – 3x² – 17x + 32 is divided by polynomial (x – 2) ?

If x⁴ – 2x³ + 3x² – 2x + 3 is divided by (3x - 2), then the remainder is-

If expression (Px³ + 3x² – 3) and (2x³ – 5x + P) is divided by (x – 4) then we get same remainder in both cases then find the value of P.

The polynomial f(x) = x⁴+2x³+3x²-ax-b when divided by x-1 and x+1 leaves the remainder 5 and 19 respectively. The value of b is:

When f(x) = x³ – 3x² + x + 2 is divided by a polynomial g(x), the quotient and remainder were x – 2 and -2x + 4 respectively. Here, g(x) is equal to

Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x−1 and it leaves remainder 6 when divided by x+1; then:

If the polynomial P(x) = 2x⁴ + x3 –5x² –x +1 is divided by the polynomial Q(x) = x² – x then the remainder is a linear polynomial R(x) = ax + b. The (a + b) equals: