Write the polynomials in index form.

(i) (1, 2, 3) (ii) (5, 0, 0, 0, $-$ 1) (iii) ( $-$ 2, 2, $-$ 2, 2)

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Solution

(i)
The coefficient form of the polynomial is (1, 2, 3).

Therefore, the index form of the polynomial is x²+ 2x + 3.

(ii)
The coefficient form of the polynomial is (5, 0, 0, 0, −1).

Therefore, the index form of the polynomial is 5x⁴+ 0x³ + 0x²+ 0x− 1 or 5x⁴− 1.

(iii)
The coefficient form of the polynomial is (−2, 2, −2, 2).

Therefore, the index form of the polynomial is −2x³ + 2x²−2x+ 2.

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