Write the polynomials in index form.

i. (1, 2, 3)

ii. (5, 0, 0, 0, -1)

iii. (-2, 2, -2, 2)

i. The given representation is the coefficient form of the polynomial. So, the first coefficient denotes the highest power of the variable.

Writing in the index form, the polynomial is:

⇒ 1.x³ + 2x² + 0.x + 3

⇒ x³ + 2x² + 3

∴ Index form of polynomial is x³ + 2x² + 3

ii. The given representation is the coefficient form of the polynomial. So the first coefficient denotes the highest power of the variable and the power of last term is always zero.

= 5.x⁴ +0.x³ + 0.x² + 0.x – 1

= 5x⁴ – 1

Therefore, the index form of the polynomial is = 5x⁴ – 1

iii. The given representation is the coefficient form of the polynomial. So the first coefficient denotes the highest power of the variable and the power of last term is always zero.

= -2.x³ + 2.x² – 2.x + 2

= -2x³ + 2x² – 2x + 2

Therefore, the index form of the polynomial is = -2x³ + 2x² – 2x + 2