Question

Which statement is true about the polynomial
–10m^4n^3 + 8m^2n^6 + 3m^4n^3 – 2m^2n^6 – 6m^2n^6 after it has been fully simplified?

It is a monomial with a degree of 4.
It is a monomial with a degree of 7.
It is a binomial with a degree of 6.
It is a binomial with a degree of 8.

Answer 1

$Given \: polynomial :\\-10m^{4}n^{3} + 8m^{2}n^{6} + 3m^{4}n^{3} - 2m^{2}n^{6} - 6m^{2}n^{6}$

/* Rearranging like terms ,we get */

$= -10m^{4}n^{3} +3m^{4}n^{3} +8m^{2}n^{6} -2m^{2}n^{6} -6m^{2}n^{6} \\= ( -10+3 )m^{4}n^{3} + ( 8 - 2 - 6 )m^{2}n^{6} \\= -7m^{4}n^{3} + 0\times m^{2}n^{6} \\ = -7m^{4}n^{3}\: ( Monomial )$

$\underline { \blue { Degree:}}$

The degree of a polynomial is the highest degree of its variable term .

$Degree \:of \: -7m^{4}n^{3} = 4 + 3 = 7$

Therefore.,

$\pink {It\: is\: a \:monomial \:with\: a \:degree \:of \:7.}$

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