Question

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

Answer 1

Answer:

(i)ans :- x^2+2x+3

(ii)ans:- 5x^4-1

Answer 2

Polynomial standard form for (1  ,2 , 3) is x² + 2x + 3

Polynomial standard form for (5, 0, 0, 0, - 1)​ is 5x⁴  - 1

Given:

• Polynomial in coefficient form (1,2,3)

• Polynomial in coefficient form (5, 0, 0, 0, - 1)

To Find:

• Polynomial in standard form

Solution:

coefficient form is  (aₙ ,  aₙ₋₁ ,..., a₁ , a₀)  for the polynomial in standard form

aₙxⁿ + aₙ₋₁xⁿ⁻¹ +...+ a₁x + a₀

Step 1:

Note that coefficient form here is (1 , 2 , 3)

hence n = 2  as there are 3 terms

a₂ = 1

a₁ = 2

a₀ = 3

Step 2:

Substituting n = 2   in aₙxⁿ + aₙ₋₁xⁿ⁻¹ +...+ a₁x + a₀

= a₂x² + a₁x¹ +a₀

Step 3:

Substituting a₂ = 1 ,  a₁ = 2 , a₀ = 3 and simplify

= 1x² +2x¹ +3

= x² + 2x + 3

Polynomial standard form for (1  ,2 , 3) is x² + 2x + 3

Similarly polynomial in standard form for (5 , 0 , 0 , -1) is

5x⁴+0x³ + 0x² + 0x  - 1

= 5x⁴ - 1

Polynomial standard form for (5, 0, 0, 0, - 1)​ is 5x⁴  - 1