Polynomials can be combined using the mathematical operations to form another polynomial. The two polynomials are: [tex]A = 2x^3 + 4x + \frac 32[/tex] and [tex]B = 2x^3- x - \frac 32[/tex]
Let the two polynomials be A and B.
The complete question is represented as:
[tex]A + B = 4x^3+3x[/tex]
[tex]A - B = 5x+3[/tex]
Add the above polynomials
[tex]A + B + A - B = 4x^3 + 3x + 5x + 3[/tex]
Collect like terms
[tex]A + A + B - B = 4x^3 + 3x + 5x + 3[/tex]
[tex]2A = 4x^3 + 8x + 3[/tex]
Divide through by 2
[tex]A = 2x^3 + 4x + \frac 32[/tex]
Make B the subject in: [tex]A + B = 4x^3+3x[/tex]
[tex]B = 4x^3 + 3x - A[/tex]
So, we have:
[tex]B = 4x^3 + 3x - [2x^3 + 4x + \frac 32][/tex]
Open brackets and collect like terms
[tex]B = 4x^3 - 2x^3+ 3x -4x - \frac 32[/tex]
[tex]B = 2x^3- x - \frac 32[/tex]
Hence, the polynomials are:
[tex]A = 2x^3 + 4x + \frac 32[/tex] and
[tex]B = 2x^3- x - \frac 32[/tex]
Read more about polynomials at:
https://brainly.com/question/11536910
