CLASS-10
REMINDER AND FACTOR THEOREM - POLYNOMIAL

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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