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Question

Find the sum of the following polynomials and write the degree of the sum so obtained

(i) 2x3 - 7x2 + 3x + 4 ; 2x3 - 3x2 + 4x + 1
(ii) 3x2 + 5x - x7 ; - 3x2 + 5x + 8
(iii) x4 + 5x3 + 7x ; 4x3 - 3x2 + 5
(iv) y2 + 2y - 5 ; y3 + 2y2 + 3y + 4 ; y3 + 7y - 2
(v) 5m2 + 3m + 8 ; m3 - 6m2 + 4m ; m3 - m2 - m + 5

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Solution

i Required polynomial = 2x3-7x2+3x+4+2x3-3x2+4x+1 = 2x3-7x2+3x+4+2x3-3x2+4x+1 = 2x3+2x3-7x2-3x2+3x+4x+4+1 =4x3-10x2+7x+5Here, the highest power is 3. Degree of the polynomial=3

iiRequired polynomial =3x2+5x-x7+-3x2+5x+8 = 3x2+5x-x7-3x2+5x+8 =-x7+3x2-3x2+5x+5x+8 =-x7+10x+8Here, the highest power is 7. Degree of the polynomial = 7

iii Required polynomial =x4+5x3+7x+4x3-3x2+5 = x4+5x3+7x+4x3-3x2+5 = x4+5x3+4x3-3x2+7x+5 = x4+9x3-3x2+7x+5Here, the highest power is 4. Degree of the polynomial = 4

iv Required polynomial =y2+2y-5+y3+2y2+3y+4+y3+7y-2 = y2+2y-5+y3+2y2+3y+4+y3+7y-2 =y3+y3+ y2+2y2+2y+3y+7y-5+4-2 =2y3+ 3y2+12y-3Here, the highest power is 3. Degree of the polynomial = 3

vRequired polynomial =5m2+3m+8+m3-6m2+4m+m3-m2-m+5 =5m2+3m+8+m3-6m2+4m+m3-m2-m+5 =m3+m3+5m2-6m2-m2+3m+4m-m+8+5 =2m3-2m2+6m+13Here, the highest power is 3. Degree of the polynomial = 3

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