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Standard IX

Mathematics

Remainder Theorem

Question 2 De...

Question

Question 2
Determine the degree of each of the following polynomials.
(i) $2 x - 1$

(ii) $- 10$

(iii) $x^{3} - 9 x + 3 x^{5}$

(iv) $y^{3} (1 - y^{4})$

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Solution

(i) The degree of the polynomial $2 x - 1$ is one because the highest exponent of x is one.

(ii) The degree of the polynomial $- 10 o r - 10 x^{0}$ is zero because the exponent of x is zero.

(iii) The degree of the polynomial $x^{3} - 9 x + 3 x^{5}$ is five because the highest exponent of x is five.

(iv) Degree of polynomial $y^{3} (1 - y^{4})$ or $y^{3} - y^{7}$ is seven because the highest exponent of y is 7.

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Question 2
Determine the degree of each of the following polynomials.
(i) $2 x - 1$

(ii) $- 10$

(iii) $x^{3} - 9 x + 3 x^{5}$

(iv) $y^{3} (1 - y^{4})$

Determine the degree of each of the following polynomials.

(i) $\frac{4 x - 5 x^{2} + 6 x^{3}}{2 x}$

(ii) $y^{2} (y - y^{3})$

(iii) $(3 x - 2) (2 x^{3} + 3 x^{2})$

Q. Question 1
Determine which of the following polynomials has (x+1) a factor:
(i)

x^{3} + x^{2} + x + 1

(ii)

x^{4} + x^{3} + x^{2} + x + 1

(iii)

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

(iv)

x^{3} - x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

Determine which of the following polynomials have $(x + 1)$ as a factor: [2 MARKS]
(i) $x^{3} + x^{2} + x + 1$
(ii) $x^{4} + x^{3} + x^{2} + x + 1$

Q. Solve the following simultaneous equations.

(i)

\frac{x}{3} + \frac{y}{4} = 4; \frac{x}{2} - \frac{y}{4} = 1

(ii)

\frac{x}{3} + 5 y = 13; 2 x + \frac{y}{2} = 19

(iii)

\frac{2}{x} + \frac{3}{y} = 13; \frac{5}{x} - \frac{4}{y} = - 2

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Remainder Theorem

Standard IX Mathematics

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Question 2 Determine the degree of each of the following polynomials. (i) 2x−1 (ii) −10 (iii) x3−9x+3x5 (iv) y3(1–y4)

Question 2
Determine the degree of each of the following polynomials.
(i) $2 x - 1$

(ii) $- 10$

(iii) $x^{3} - 9 x + 3 x^{5}$

(iv) $y^{3} (1 - y^{4})$