Question

Express the following polynomials in the coefficient form:

(i) 2x² + 5x + 12
(ii) y⁴ $-$ 3y² + 2y $-$ 7
(iii) x⁵ + 3x²
(iv) y⁴ $-$ 3
(v) 9x

Answer 1

(i) The degree of the given polynomial is 2.
∴ Number of terms in the index form of the polynomial = 2 + 1 = 3
The polynomial $2x^2+5x+12$ can be written in the index form as $2x^2+5x+12$.
∴ The coefficient form of the given polynomial is (2, 5, 12).

(ii) The degree of the given polynomial is 4.
∴ Number of terms in the index form of the polynomial = 4 + 1 = 5
The polynomial $y^4-3y^2+2y-7$ can be written in the index form as $y^4+0y^3-3y^2+2y-7$.
∴ The coefficient form of the given polynomial is (1, 0, $-$ 3, 2, $-$ 7).

(iii) The degree of the given polynomial is 5.
∴ Number of terms in the index form of the polynomial = 5 + 1 = 6
The polynomial $x^5+3x^2$ can be written in the index form as $x^5+0x^4+0x^3+3x^2+0x+0$.
∴ The coefficient form of the given polynomial is (1, 0, 0, 3, 0, 0).

(iv) The degree of the given polynomial is 4.
∴ Number of terms in the index form of the polynomial = 4 + 1 = 5
The polynomial $y^4-3$ can be written in the index form as $y^4+0y^3+0y^2+0y-3$.
∴ The coefficient form of the given polynomial is (1, 0, 0, 0, $-$3).

(v) The degree of the given polynomial is 1.
∴ Number of terms in the index form of the polynomial = 1 + 1 = 2
The polynomial $9x$ can be written in the index form as $9x+0$
∴ The coefficient form of the given polynomial is (1, 0).