Discuss: Degrees of Sums and Products of Polynomials Make up several pairs of polynomials, then calculate the sum and product of each pair. Then answer the following questions.

zi2lalZ

zi2lalZ

Answered question

2021-08-06

DISCUSS: 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

Viktor Wiley

Viktor Wiley

Skilled2021-08-07Added 84 answers

Step 1
To explain the given problem
Step 2
a) The degree of the product is just double of the original polynomial.Multiplying the parantheses a product involving the leading power of both will emerge.
for examle (x21),(x2+1)
product of polynomial
=(x21)(x2+1)
=x41
b) The degree of a sum is atmost the largest of the degrees. But it could be smaller either (if the leading powers cancel.) for example x2 and (x2+x)
sum of polynomial
=x2x2+x
=x
c) given that the two polynomials
2x3+x3 and 2x3x+7
product of polynomials
=(2x3+x3)(2x3x+7)
=4x64x4+20x3x2+10x21
sum of polynomial
=2x3+x32x3x+7
=4

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