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Question

Determine the degree of each of the following polynomials.
(i) 4x-5x2+6x32x
(ii) y2(y – y3)
(iii) (3x – 2) (2x3 + 3x2)
(iv) -12x+3
(v) – 8
(vi) x–2(x4 + x2)

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Solution


(i) 4x-5x2+6x32x=4x2x-5x22x+6x32x=2-52x+3x2
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) -12x+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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