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  • For the polynomial \frac{x^{3}+2x+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

For the polynomial \frac{x^{3}+2x+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

Answers (1)

(i) 6

(ii) \frac{1}{5}

(iii) -1

(iv) \frac{1}{5}

Solution           

\frac{x^{3}+2x+1}{5}-\frac{7}{2}x^{2}-x^{6}\\ =\frac{x^{3}}{5}+\frac{2x}{5}+\frac{1}{5}-\frac{7x^{2}}{2}-x^{6}\\ =-x^{6}+\frac{x^{3}}{5}-\frac{7x^{2}}{2}+\frac{2x}{5}+\frac{1}{5}\\ =(-1)x^{6}+\left (\frac{1}{5} \right )x^{3}-\left (\frac{7}{2} \right )x^{2} +\left (\frac{2}{5} \right )x+\frac{1}{5}\\

(i) Degree of polynomial: Degree of polynomial is the highest power of the polynomial’s monomial with non-zero coefficient

Here the highest degree of x is 6 therefore the degree of the polynomial is six. 

(ii) The coefficient of x^{3}

Here \frac{1}{5} is multiplied by x^{3} therefore coefficient of x^{3} is \frac{1}{5}

(iii) The coefficient of x^{6}

Here –1 is multiplied by x^{6} therefore coefficient of x^{6} is –1.

(iv) The constant term

The constant term is the one without the variable x.

So, \frac{1}{5} is the constant term

Posted by

infoexpert24

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