Q. 65.0( 1 Vote )

# Find out the degree of the polynomials and the leading coefficients of the polynomials given below:

(i)

(ii) 13x^{3} – x^{13} – 113

(iii) -77 + 7x^{2} – x^{7}

(iv) -181 + 0.8y – 8y^{2} + 115y^{3} + y^{8}

(v) x^{7} – 2x^{3}y^{5} + 3xy^{4} – 10xy + 10

Answer :

(i) The monomials in the polynomial are called the terms. The highest power of the terms is the degree of the polynomial.

x^{2} – 2x^{3} + 5x^{7} – x^{3} – 70x – 8 is a polynomial in x. Here we have 6 monomials x^{2}, – 2x^{3}, + 5x^{7}, –x^{3}, –70x and –8 which are called the terms of the polynomial.

The highest power is 7 so the **degree of the polynomial is 7**.

(ii) 13x^{3} – x^{13} – 113 is a polynomial in x. Here we have 3 monomials and the highest power is 13 so the **degree of the polynomial is 13.**

(iii) -77 + 7x^{2} – x^{7} is a polynomial in x. Here we have 3 monomials and the highest power is 7 so the **degree of the polynomial is 7**.

(iv) -181 + 0.8y – 8y^{2} + 115y^{3} + y^{8} is a polynomial in x. Here we have 5 monomials and the highest power is 8 so the **degree of the polynomial is 8**.

(v) x^{7} – 2x^{3}y^{5} + 3xy^{4} – 10xy + 10 is a polynomial in x and y, Here we have 5 monomials.

**Term 1:** x^{7} variable x, power of x is 7. Hence the power of the term is **7**.

**Term 2:** – 2x^{3}y^{5} the variables are x and y; the power of x is 3 and the power of y is 5.

Hence the power of the term – 2x^{3}y^{5} is 3 + 5 = **8** [Sum of the exponents of variables x and y ].

**Term 3:** 3xy^{4} the variables are x and y; the power of x is 1 and the power of y is 4.

Hence the power of the term 3xy^{4} is 1 + 4 = **5** [Sum of the exponents of variables x and y].

**Term 4:** – 10xy the variables are x and y; the power of x is 1 and the power of y is 1.

Hence the power of the term -10xy is 1 + 1 = **2** [Sum of the exponents of variables x and y].

**Term 5:** 10 the constant term and it can be written as 10x^{0}y^{0}. The power of the variables x^{0}y^{0} is zero. Hence the power of the term 10 is **0**.

So the highest power is 8, hence the **degree of the polynomial is 8.**

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Find the product of the following pairs of monomials:

i. 3, 7x

ii. – 7x, 3y

iii. – 3a, 5ab

iv. 5a^{2}, – 4a

v.

vi. Xy^{2}, x^{2}y

vii. x^{3}y^{5}, xy^{2}

viii. abc, abc

ix. xyz. x^{2}yz

x. a^{2}b^{2}c^{3}, abc^{2}

Find the product of the following :

(x + y + z) (x + y – z)

Tamilnadu - Math Term-2Find the product of the following :

(2x + 3y) (x^{2} – xy + y^{2})

Find the product of the following :

(a + b) (2a^{2} – 5ab + 3b^{2})

Find the product :

(i) (a^{3}) × (2a^{5}) × (4a^{15})

(ii) (5 – 2x) (4 + x)

(iii) (x + 3y) (3x – y)

(iv) (3x + 2) (4x – 3)

(v)

Tamilnadu - Math Term-2Find out the product :

(i) 2a, 3a^{2}, 5a^{4}

(ii) 2x, 4y, 9z

(iii) ab, bc, ca

(iv) m, 4m, 3m^{2}, - 6m^{3}

(v) xyz, y^{2}z, yx^{2}

(vi) lm^{2}, mn^{2}, ln^{2}

(vii) -2p, -3q, -5p^{2}

Complete the following table of products:

Tamilnadu - Math Term-2

Find the product of the following :

(m – n) (m^{2} + mn + n^{2})

Find the product of the following :

(a + b) (a^{2} + 2ab + b^{2})