Write the index form of the polynomial using variable x from its coefficient form.

i. (3, -2, 0, 7, 18)

ii. (6, 1, 0, 7)

iii. (4, 5, -3, 0)

i. 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.

So the index form is as follows:

3x⁴ – 2x³ + 0x² + 7x + 18

= 3x⁴ – 2x³ + 7x + 18

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.

So the index form is as follows:

6x³ + x² + 0x + 7

=6x³ + x² + 7

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.

So the index form is as follows:

4x³ + 5x² -3x + 0

= 4x³ + 5x² -3x