Question

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Answer 1

Answer:

i) The degree of polynomial is 6

ii) The coefficient of x³ is 1/5

iii) The coefficient of x^6 is -1

iv) The constant term is +1/5.

Step-by-step explanation:

Polynomial:

$\sf \longrightarrow \: \dfrac{ {x}^{3} + 2x + 1}{5} - \dfrac{7}{2} {x}^{2} - {x}^{6}$

i) Degree of polynomial :-

The above equation has :-

→ seperating term....

x^3/5 + 2x/5 +1/5 - 7/2x² - x^6

Ans -> 6

A degree of polynomial is the highest power a polynomial has.

ii) Coefficient of x³ :-

Ans -> 1/5

A coefficient is a number that a variable is multiplied with. Here , in this case there is a number 1/5 which x³ holds , so the coefficient remains as 1/5.

iii) Coefficient of x^6

Ans -> (-1)

here in this case there is no number wch x^6 holds , so the coefficient remains as - 1.

iv) Constant term

Ans -> +1/5

A constant term is a term with no variable. so here in this case "1/5" does not hold any variable so here the constant tem is 1/5.

What you need to know ?

Polynomial : A variable bases language in maths. or A string of variables and numbers put together.

Degree of polynomial : Highest power of a polynomial is called degree of polynomial.

Coefficient : A number by which a variable is multiplied.

Constant : It's a numerical term holding no variable.

Answer 2

$\large\bf\underbrace{\red{SOLUTION:-}}$

GIVEN :-

$\large\rm{\boxed{\dfrac{x^3\:+\:2x\:+\:1}{5}\:-\:\dfrac{7}{2}\:x^2\:-\:x^6\:}}$

▼ we also write the above polynomial as,

$\large\rm{=\:\dfrac{1}{5}x^3\:+\:\dfrac{2}{5}x\:+\:\dfrac{1}{5}\:-\:\dfrac{7}{2}x^2\:-\:x^6\:}$

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(i) The degree of polynomial :-

• The highest power of Polynomial is the degree of polynomial .

$\checkmark\:\bf\underline{\orange{\boxed{Degree\:of\:Polynomial\:is\:6\:}}}$

(ii) Coefficient of x³ :-

$\checkmark\:\bf\underline{\green{\boxed{Coefficient\:of\:x^3\:is\:(\dfrac{1}{5})\:}}}$

(iii) Coefficient of $\bold{x^6}$ :-

$\checkmark\:\bf\underline{\purple{\boxed{Coefficient\:of\:x^6\:is\:(-1)\:}}}$

(iv) Constant term :-

$\checkmark\:\bf\underline{\blue{\boxed{Constant\:term\:is\:(\dfrac{1}{5})\:}}}$