Degrees of Sums and Products of Polynomials.Make up several pairs of polynomials, then calculate the sum and product of each pair.

a2linetagadaW

a2linetagadaW

Answered question

2021-09-02

Degrees of Sums and Products of Polynomials
Make up several pairs of polynomials, then calculate the sum and product of each pair. On the basis of your experiments and observations, answer the following questions.
a) How is the degree of the product related to the degrees of the original polynomials?
b) How is the degree of the sum related to the degrees of the original polynomials?
c) Test your conclusions by finding the sum and product of the following polynomials:
2x3+x3 and 2x3x+7

Answer & Explanation

averes8

averes8

Skilled2021-09-03Added 92 answers

a) Consider the first polynomial as (a0+a1x+a2x2++anxn).
Consider the second polynomial as (b0+b1x+b2x2++bmxm)
Here, the value of m is greater than n.
The product of the two polynomial can be expressed as,
(a0+a1x+a2x2++anxn)(b0+b1x+b2x2++bmxm)=(c0+c1x+c2x2++cmxm+n)
Here, ck=i+j=km+naibj
The degree of the product is m+n
Hence, the degree of the product is the sum of the degrees of the original polynomials.
b) Consider the first polynomial as (a0+a1x+a2x++anxn)
Consider the second polynomial as (b0+b1x+b2x2++bmxm)
Here, the value of m is greater than n.
The sum of the two polynomial can be expressed as,
(a0+a1x+a2x2++anxn)+(b0+b1x+b2x2++bmxm)=(c0+c1x+c2x2++cmxm+n)
Here, ck represents the sum of ai+bj
ck=i+j=km+nai+bj
The degree of the sum is m.
For a different case, consider the first polynomial as (a0+a1x+a2x2+anxn) and consider the second polynomial as (a0+a1x+a2x2++anxn)

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