Question

for the polynomial x³+2x+1 by 5 -7 by 2 x²-x^6

write the coefficient of x³
write the coefficient of x^6
the constant term
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Answer 1

The given polynomial is,

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

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

(1) Degree of the polynomial is the Highest degree of its terms, which is 6 in this case (degree of $x^6)$

$\bold{(2) Coefficient \: of \: {x}^{3} \: is \: \frac{1}{5} }$

$\bold{(3) \: Coefficient \: of \: {x}^{6} \: is \: - 1}$

(4) The constant term in the polynomial is $\frac{1}{5}$