Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients:

(1) a = 6, b = 17, c = 11

(2) a = 1, b = —1, c = —1, d = 1

(3) a = 5, b = 7, c = 2

(4) a = 1, b = —3, c = —1, d = 3

(5) a = 3, b = —5, c = —11, d = —3

(1) The quadratic polynomial is,

p(x) = ax² + bx + c; a ≠ 0, a, b, c ε R.

∴ Substituting a = 6, b = 17 and c = 11, we get the required quadratic polynomial

p(x) = 6x² + 17x + 11.

(2) The cubic polynomial is,

p(x) = ax³ + bx² + cx + d; a ≠ 0, a, b, c, d ε R.

∴ Substituting a = 1, b = —1, c = —1 and d = 1, we get the required cubic polynomial

p(x) = x³ – x² – x + 1.

(3) The quadratic polynomial is,

p(x) = ax + bx + c; a ≠ 0, a, b, c ε R.

∴ Substituting a = 5, b = 7 and c = 2, we get the required quadratic polynomial

p(x) = 5x² + 7x + 2.

(4) The cubic polynomial is,

p(x) = ax + bx + cx + d; a ≠ 0, a, b, c, d ε R.

∴ Substituting a = 1, b = –3, c = –1 and d = 3, we get the required cubic polynomial

p(x) = x³ – 3x² – x + 3.

(5) The cubic polynomial is,

p(x) = ax³ + bx² + cx + d; a ≠ 0, a, b, c, d ε R.

∴ Substituting a = 3, b = –5, c = –11 and d = –3, we get the required cubic polynomial

p(x) = 3x³ – 5x² – 11x – 3.