Write the polynomials in index form. i. (1, 2, 3) ii. (5, 0, 0, 0 ,-

1.	Write the polynomials in index form. i. (1, 2, 3) ii. (5, 0, 0, 0 ,-1) iii. (-2, 2, -2, 2)
Answer» i. Number of coefficients = 3 ∴ Degree = 3 – 1 = 2 ∴ Taking x as variable, the index form is x² + 2x + 3 ii. Number of coefficients = 5 ∴ Degree = 5 – 1=4 ∴ Taking x as variable, the index form is 5x⁴ + 0x³+ 0x² + 0x – 1 iii. Number of coefficients = 4 ∴Degree = 4 – 1 = 3 ∴Taking x as variable, the index form is -2x³ + 2x²– 2x + 2

Write the polynomials in index form. i. (1, 2, 3) ii. (5, 0, 0, 0 ,-1) iii. (-2, 2, -2, 2)

Answer»

i. Number of coefficients = 3

∴ Degree = 3 – 1 = 2

∴ Taking x as variable, the index form is x² + 2x + 3

ii. Number of coefficients = 5

∴ Degree = 5 – 1=4

∴ Taking x as variable, the index form is 5x⁴ + 0x³+ 0x² + 0x – 1

iii. Number of coefficients = 4

∴Degree = 4 – 1 = 3

∴Taking x as variable, the index form is -2x³ + 2x²– 2x + 2