Polynomial –
An expression of the form –
f(x) = aₒxᵉ + a₁xᵉˉ¹ + a₂xᵉˉ² + ……………… + aₑ₋₁x + aₑ
where aₒ, a₁, a₂,…………, aₑ₋₁, aₑ are real numbers and aₒ ≠ 0, is called a polynomial of degree ‘e’.
(i) Here aₒxᵉ is called the leading term and aₒ is called the leading coefficient of the polynomial f(x)
(ii) aₒ, a₁, a₂,……………, aₑ₋₁ are called the coefficient of xᵉ, xᵉˉ¹, xᵉˉ²,…………., x respectively. Also, aₑ is known as the constant term of polynomial f(x).
(iii) We denote a polynomial in x by f(x), g(x), h(x), p(x), q(x), r(x), etc.
Example. (i) f(x) = (7x + 12) is a polynomial in x of degree 1
(ii) g(x) = (6x²- 12x + 7) is a polynomial in x of degree 2.
(iii) f(y) = (8y³ + 12x² - 7x – 9) is a polynomial in y of degree 3.
(iv) f(z) = (z⁴ - 3z³ + 15z² - 8z + 12) is a polynomial in z of degree 4.
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