Verify that 3, ‒2, 1 are the zeros of the cubic polynomial p(x) = x³ – 2x² – 5x + 6 and verify the relation between its zeros and coefficients.

Verify that 5, –2 and are the zeros of the cubic polynomial p(x) = 3x³ - 10x²– 27x + 10 and verify the relation between its zeros and coefficients

Find a cubic polynomial whose zeros are 2, –3 and 4

Find a cubic polynomial whose zeros are , 1 and –3.

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, –2 and –24 respectively.

Find the quotient and the remainder when:

f(x) = x³ – 3x² + 5x –3 is divided by g(x) = x² – 2.

Find the quotient and the remainder when:

f(x) = x⁴ – 3x² + 4x + 5 is divided by g(x) = x² + 1 – x.

Find the quotient and the remainder when:

f(x) = x⁴ – 5x + 6 is divided by g(x) = 2 – x².

By actual division, show that x³ – 3 is a factor 2x⁴ + 3x³ – 2x² – 9x – 12.

On dividing 3x³ + x² + 2x + 5 by a polynomial g(X), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).

Verify division algorithm for the polynomials f(x) = 8 + 20x + x² ‒ 6x³ and g(x) = 2 + 5x ‒ 3x².

It is given that ‒1 is one of the zeros of the polynomial x³ + 2x² ‒ 11x ‒ 12. Find all the zeros of the given polynomial.

If 1 and ‒2 are two zeros of the polynomial (x³ ‒ 4x² ‒ 7x + 10), find its third zero.

If 3 and ‒3 are two zeros of the polynomial (x⁴ + x³ ‒ 11x² ‒ 9x + 18), find all the zeros of the given polynomial.

If 2 and ‒2 are two zeros of the polynomial (X⁴ + x³ ‒ 34x² ‒ 4x + 120), find all the zeros of the given polynomial.

Find all the zeros of (x⁴ + x³ ‒ 23x² ‒ 3x + 60), if it is given that two of its zeros are √3 and ‒√3.

Find all the zeros of (2x⁴ ‒ 3x³ ‒ 5x² + 9x ‒ 3), it being given that two of its zeros are √3 and – √3.

Obtain all other zeros of (x⁴ + 4x³ ‒ 2x² ‒ 20x ‒15) if two of its zeros are √5 and – √5.

Find all the zeros of the polynomial (2x⁴ ‒ 11x³ + 7x² + 13x ‒ 7), it being given that two of its zeros are (3 + √3) and (3 ‒ √3)