Writei the coefficient of x 3 in x-3 x 2-5 x 3-x 4-ii the coefficient of x in 3-22 x-6 x 2 -iii the coefficient of x2 in 2 x-3-x3-iv the coefficient of x in 38 - 2-27 x-16-v the constant term in - 2 x 2-7 x -25 -

(i) The coefficient of x3 nbsp;in nbsp;x+3x2 5x3+x4 nbsp;is nbsp; minus;5. (ii) The coefficient of nbsp;x in nbsp;3 22x+6x2 nbsp;is nbsp; 22. ...

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Byju's Answer

Standard VIII

Mathematics

Multiplication of Any Polynomial

Writei the co...

Question

Write
(i) the coefficient of $x^{3} in x + 3 x^{2} - 5 x^{3} + x^{4}$ .
(ii) the coefficient of x in $\sqrt{3} - 2 \sqrt{2} x + 6 x^{2}$ .
(iii) the coefficient of x² in 2x – 3 + x³.
(iv) the coefficient of x in $\frac{3}{8} x^{2} - \frac{2}{7} x + \frac{1}{6}$ .
(v) the constant term in $\frac{π}{2} x^{2} + 7 x - \frac{2}{5} π$ .

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Solution

(i) The coefficient of x³ in $x + 3 x^{2} - 5 x^{3} + x^{4}$ is −5.

(ii) The coefficient of x in $\sqrt{3} - 2 \sqrt{2} x + 6 x^{2}$ is $- 2 \sqrt{2}$ .

(iii) 2x – 3 + x³= – 3 + 2x + 0x²+ x³
The coefficient of x² in 2x – 3 + x³ is 0.

(iv) The coefficient of x in $\frac{3}{8} x^{2} - \frac{2}{7} x + \frac{1}{6}$ is $- \frac{2}{7}$ .

(v) The constant term in $\frac{π}{2} x^{2} + 7 x - \frac{2}{5} π$ is $- \frac{2}{5} π$ .

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Similar questions

Write

(i) the coefficient of $x^{3}$ in $x + 3 x^{2} - 5 x^{3} + x^{4}$

(ii) the coefficient of $x$ in $\sqrt{3} - 2 \sqrt{2} x + 6 x^{2}$

(iii) the coefficient of $x^{2}$ in $2 x - 3 + x^{3}$

(iv) the coefficient of $x$ in $\frac{3}{8} x^{2} - \frac{2}{7} x + \frac{1}{6}$

(v) the constant term in $\frac{π}{2} x^{2} + 7 x - \frac{2}{5} π$

Q. Write:
(i) Coefficient of x³ in 2x + x² − 5x³ + x⁴
(ii) Coefficient of x in

\sqrt{3} - 2 \sqrt{2} x + 4 x^{2}

.
(iii) Coefficient of x² in

\frac{π}{3} x^{2} + 7 x - 3

.
(iv) Coefficient of x² in 3x − 5

Q. For

\frac{x^{3} + 2 x + 1}{5} - \frac{7}{2} x^{2} - x^{6}

, write
i) the degree of the polynomial
ii) the coefficient of

x^{3}

iii) the coefficient of

x^{6}

iv) the constant term

Q. The coefficient of

x^{n}

(1 - x + \frac{x^{2}}{2!} - \frac{x^{3}}{3!} + . . . - \frac{(- 1)^{n} x^{n}}{n!})^{2} s e q u a l t o

Find the coefficient of $x^{15}$ in $(x^{3} + x^{6} + x^{9} + . . . . . . . . . . .) (x^{2} + x^{4} + x^{6} + . . . . . . . . . . .) (x + x^{2} + x^{3} + . . . . . . . . . .)$

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Write (i) the coefficient of x3 in x+3x2-5x3+x4. (ii) the coefficient of x in 3-22x+6x2. (iii) the coefficient of x2 in 2x – 3 + x3. (iv) the coefficient of x in 38x2-27x+16. (v) the constant term in π2x2+7x-25π.

(i) The coefficient of x3 in x+3x2-5x3+x4 is −5. (ii) The coefficient of x in 3-22x+6x2 is -22. (iii) 2x – 3 + x3 = – 3 + 2x + 0x2 + x3 The coefficient of x2 in 2x – 3 + x3 is 0. (iv) The coefficient of x in 38x2-27x+16 is -27. (v) The constant term in π2x2+7x-25π is -25π.