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Degree of a Polynomial

Find the sum ...

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

$(i) Required polynomial = (2 x^{3} - 7 x^{2} + 3 x + 4) + (2 x^{3} - 3 x^{2} + 4 x + 1) = 2 x^{3} - 7 x^{2} + 3 x + 4 + 2 x^{3} - 3 x^{2} + 4 x + 1 = 2 x^{3} + 2 x^{3} - 7 x^{2} - 3 x^{2} + 3 x + 4 x + 4 + 1 = 4 x^{3} - 10 x^{2} + 7 x + 5 Here, the highest power is 3 . ∴ Degree of the polynomial = 3$

$(ii) Required polynomial = (3 x^{2} + 5 x - x^{7}) + (- 3 x^{2} + 5 x + 8) = 3 x^{2} + 5 x - x^{7} - 3 x^{2} + 5 x + 8 = - x^{7} + 3 x^{2} - 3 x^{2} + 5 x + 5 x + 8 = - x^{7} + 10 x + 8 Here, the highest power is 7 . ∴ Degree of the polynomial = 7$

$(iii) Required polynomial = (x^{4} + 5 x^{3} + 7 x) + (4 x^{3} - 3 x^{2} + 5) = x^{4} + 5 x^{3} + 7 x + 4 x^{3} - 3 x^{2} + 5 = x^{4} + 5 x^{3} + 4 x^{3} - 3 x^{2} + 7 x + 5 = x^{4} + 9 x^{3} - 3 x^{2} + 7 x + 5 Here, the highest power is 4 . ∴ Degree of the polynomial = 4$

$(iv) Required polynomial = (y^{2} + 2 y - 5) + (y^{3} + 2 y^{2} + 3 y + 4) + (y^{3} + 7 y - 2) = y^{2} + 2 y - 5 + y^{3} + 2 y^{2} + 3 y + 4 + y^{3} + 7 y - 2 = y^{3} + y^{3} + y^{2} + 2 y^{2} + 2 y + 3 y + 7 y - 5 + 4 - 2 = 2 y^{3} + 3 y^{2} + 12 y - 3 Here, the highest power is 3 . ∴ Degree of the polynomial = 3$

$(v) Required polynomial = (5 m^{2} + 3 m + 8) + (m^{3} - 6 m^{2} + 4 m) + (m^{3} - m^{2} - m + 5) = 5 m^{2} + 3 m + 8 + m^{3} - 6 m^{2} + 4 m + m^{3} - m^{2} - m + 5 = m^{3} + m^{3} + 5 m^{2} - 6 m^{2} - m^{2} + 3 m + 4 m - m + 8 + 5 = 2 m^{3} - 2 m^{2} + 6 m + 13 Here, the highest power is 3 . ∴ Degree of the polynomial = 3$

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Similar questions

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

2 x^{3} - 7 x^{2} + 3 x + 4; 2 x^{3} - 3 x^{2} + 4 x + 1

Find the sum of the following polynomials :

x^{4} + 5 x^{3} + 7 x; 4 x^{3} - 3 x^{2} + 5

Find the sum of the following polynomials:

5 m^{2} + 3 m + 8; m^{3} - 6 m^{2} + 4 m; m^{3} - m^{2} - m + 5

Find the sum of the following polynomials

y^{2} + 2 y - 5; y^{3} + 2 y^{2} + 3 y + 4; y^{3} + 7 y - 2

Divide each of the following polynomials by synthetic division method and also by

linear division method. Write the quotient and the remainder.

(i)

(2 m^{2} - 3 m + 10) \div (m - 5)

(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)

(y^{3} - 216) \div (y - 6)

(2 x^{4} + 3 x^{3} + 4 x - 2 x^{2}) \div (x + 3)

(x^{4} - 3 x^{2} - 8) \div (x + 4)

(y^{3} - 3 y^{2} + 5 y - 1) \div (y - 1)

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