Answer:
The remainder is -2.
Step-by-step explanation:
According to the Polynomial Remainder Theorem, if we divide a polynomial P(x) by a binomial (<em>x</em> - <em>a</em>), then the remainder of the operation will be given by P(a).
Our polynomial is:
And we want to find the remainder when it's divided by the binomial:
We can rewrite our divisor as (<em>x</em> - (-1)). Hence, <em>a</em> = -1.
Then by the PRT, the remainder will be:
The remainder is -2.
Degree of a polynomial gives the highest power of its terms. Yes there is a difference between the degrees of sum and difference of the polynomials.
<h3>What is degree of a polynomial?</h3>Degree of a polynomial is the highest power that its terms pertain(for multi-variables, the power of term is addition of power of variables in that term).
Thus, in , the degree of the polynomial is 3 as the highest power in its terms is 3.
(power and exponent are same thing)
<h3>What are like terms?</h3>Those terms which have same variables raised with same powers.
For example, and
are like terms since variable is same, and it is raised to same power 3.
For example and
are not like terms as the variables are same but powers aren't same.
The given polynomials are:
Their sum is
(only like terms' coefficients can be added (or subtracted) for addition or subtraction of them )
The sum's degree is 7
Their difference is:
Difference's degree is 5
Thus, both's degrees are not same.
Thus, Yes there is a difference between the degrees of sum and difference of the polynomials.
Learn more about subtraction of polynomials here: