Question

Express the following polynomials in the index form taking 'x' as a variable.

(i) (3, 2, 7)
(ii) (2, 0, 0, $-$4)
(iii) (1, 0, $-$3, 1, 5)
(iv) ($-$2, 3, $-$5, 6)
(v) ( 1, 0, 0, 0, 0, 0, 64)

Answer 1

(i) The polynomial (3, 2, 7) contains 3 coefficients.
i.e., degree of the polynomial = 3 $-$ 1 = 2
∴ The index form of the given polynomial is 3x² + 2x + 7.

(ii) The polynomial (2, 0, 0,$-$ 4) contains 4 coefficients.
i.e., degree of the polynomial = 4 $-$ 1 = 3
∴ The index form of the given polynomial is 2x³ + 0 x² + 0 x $-$ 4.

(iii) The polynomial (1, 0, $-$ 3, 1, 5) contains 5 coefficients.
i.e., degree of the polynomial = 5 $-$ 1 = 4
∴ The index form of the given polynomial is x⁴ + 0 x³ $-$3 x² + x + 5.

(iv) The polynomial ($-$2, 3, $-$ 5, 6) contains 4 coefficients.
i.e., degree of the polynomial = 4 $-$ 1 = 3
∴ The index form of the given polynomial is $-$2x³ + 3x² $-$5 x + 6.

(v) The polynomial (1, 0, 0, 0, 0, 0, 64) contains 7 coefficients.
i.e., degree of the polynomial = 7 $-$ 1 = 6
∴ The index form of the given polynomial is x⁶ + 0 x⁵ + 0 x⁴ + 0 x³ + 0 x² + 0 x + 64.