Question

# Determine the degree of each of the following polynomials. (i) $\frac{4x-5{x}^{2}+6{x}^{3}}{2x}$ (ii) y2(y – y3) (iii) (3x – 2) (2x3 + 3x2) (iv) $-\frac{1}{2}x+3$ (v) – 8 (vi) x–2(x4 + x2)

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Solution

## (i) $\frac{4x-5{x}^{2}+6{x}^{3}}{2x}=\frac{4x}{2x}-\frac{5{x}^{2}}{2x}+\frac{6{x}^{3}}{2x}=2-\frac{5}{2}x+3{x}^{2}$ Here, the highest power of x is 2. So, the degree of the polynomial is 2. (ii) y2(y – y3) = y3 – y5 Here, the highest power of y is 5. So, the degree of the polynomial is 5. (iii) (3x – 2)(2x3 + 3x2) = 6x4 + 9x3 – 4x3 – 6x2 = 6x4 + 5x3 – 6x2 Here, the highest power of x is 4. So, the degree of the polynomial is 4. (iv) $-\frac{1}{2}x+3$ Here, the highest power of x is 1. So, the degree of the polynomial is 1. (v) – 8 –8 is a constant polynomial. So, the degree of the polynomial is 0. (vi) x–2(x4 + x2) = x2 + x0 = x2 + 1 Here, the highest power of x is 2. So, the degree of the polynomial is 2.

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