Question

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)​

Answer 1

Given :   polynomial in coefficient form

(i) (3, -2, 0, 7, 18) ii)(6,1,0,7)​

To Find : Index form using variable 'x' as.​

Solution:

coefficient form is  (aₙ ,  aₙ₋₁ , ______ a₁ , a₀)  for variable x  

aₙxⁿ + aₙ₋₁xⁿ⁻¹ +______+ a₁x + a₀    

(i) (3, -2, 0, 7, 18) comparing with  (aₙ ,  aₙ₋₁ , ______., a₁ , a₀)

a₀ = 18

a₁ = 7

a₂ = 0

a₃ = -2

a₄ = 3

index form

= 3.x⁴ - 2.x³ + 0.x² + 7.x  + 18

= 3x⁴  -2x³ + 7x + 18

3x⁴  -2x³ + 7x + 18 is the index form of polynomial for  (3, -2, 0, 7, 18) coefficient form.

6x³ + x²  + 7 is index form for (6,1,0,7)​

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