Using a suitable identity, determine the value of (17)³ + (-12)³ + (-5)³

If (x – 1/x) = 4, then evaluate (x² + 1/x²) and (x⁴ + 1/x⁴).

Factorise 64m³ – 343n³

Factorise 8a³ + b³ + 12a²b + 6ab²

Without actual division, prove that 2x^4 – 5x^3 + 2x^2 – x + 2 is divisible by x^2 – 3x + 2.

Evaluate (102)^3 using a suitable identity.

Factorise x^2 – 1 – 2a – a^2.

Check whether (7 + 3x) is a factor of (3x^3 + 7x).

Find the values of a and b so that (2x^3 + a x^2 + x + b) has (x + 2) and (2x – 1) as factors.

Find the value of x^3 + y^3 + z^3 – 3xyz if x + y + z = 15 and x^2 + y^2 + z^2 = 83

Calculate the perimeter of a rectangle whose area is 25x^2 - 35x + 12

Give an example of a monomial and a binomial having degrees of 82 and 99, respectively.

The value of 104 × 96 is

The value of 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37 is

If one of the factor of x² + x – 20 is (x + 5). Find the other

If x + 2 is a factor of x³ – 2ax² + 16, then value of a is

Find the product: (x – 3y) (x + 3y) (x² + 9y²)

Factorise: (a – b)³ + (b – c)³ + (c – a)³

If x + y = 12 and xy = 32, Find the value of x² + y²

Find the value of x³ + y³ + z³ – 3xyz if x² + y² + z² = 83 and x + y + z = 15

Find the value of 9x² + 4y² if xy = 6 and 3x + 2y = 12.

Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2, respectively. Also find its zeroes.

α and β are zeroes of the quadratic polynomial x² – 6x + y. Find the value of ‘y’ if 3α + 2β = 20

Find the quadratic polynomial if its zeroes are 0 and √5.

Find the zeroes of the polynomial 4x^2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.

Find the value of "p" from the polynomial x² + 3x + p, if one of the zeroes of the polynomial is 2.

If the product of zeroes of the polynomial p(x)=3x² + kx − 2 is 2/3 ​, find the value of k.

If the zeroes of the quadratic polynomial p(x) = ax² + bx + c are reciprocal of each other, prove that c = a.

Find a quadratic polynomial whose zeroes are 5 and −3.

Find the zeroes of the polynomial: p(x) = x² − 7x + 10 and verify the relation between zeroes and coefficients.

If one zero of the polynomial (a² + 9)x² + 13x + 6a is the reciprocal of the other, find the value of a.