Answer:
a) We get [tex]\mathbf{A+B=x^2-2x+1}[/tex]
So, Is the result of A+B is a polynomial:Yes
b) We get [tex]\mathbf{A-B=6x^3-7x^2+2x-1}[/tex]
So, Is the result of A-B is a polynomial:Yes
c) We get [tex]\mathbf{A.B=9x^6+21x^5-18x^4+9x^3-3x^2}[/tex]
So, Is the result of A.B is a polynomial:Yes
Step-by-step explanation:
We are giving the polynomial equations:
[tex]A= 3x^2(x-1)\\B=-3x^3+4x^2-2x+1[/tex]
We need to find
a) A+B
[tex]A+B=3x^2(x-1)+(-3x^3+4x^2-2x+1)\\A+B=3x^3-3x^2-3x^3+4x^2-2x+1\\A+B=3x^3-3x^3-3x^2+4x^2-2x+1\\A+B=x^2-2x+1\\[/tex]
So, we get [tex]\mathbf{A+B=x^2-2x+1}[/tex]
So, Is the result of A+B is a polynomial:Yes
b) A-B
[tex]A-B=3x^2(x-1)-(-3x^3+4x^2-2x+1)\\A-B=3x^3-3x^2+3x^3-4x^2+2x-1\\A-B=3x^3+3x^3-3x^2-4x^2+2x-1\\A-B=6x^3-7x^2+2x-1\\[/tex]
So, we get [tex]\mathbf{A-B=6x^3-7x^2+2x-1}[/tex]
So, Is the result of A-B is a polynomial:Yes
c) A . B
[tex]A.B=3x^3(-3x^3+4x^2-2x+1)-3x^2(-3x^3+4x^2-2x+1)\\A.B=9x^6+12x^5-6x^4+3x^3+9x^5-12x^4+6x^3-3x^2\\A.B=9x^6+12x^5+9x^5-6x^4-12x^4+3x^3+6x^3-3x^2\\A.B=9x^6+21x^5-18x^4+9x^3-3x^2[/tex]
So, we get [tex]\mathbf{A.B=9x^6+21x^5-18x^4+9x^3-3x^2}[/tex]
So, Is the result of A.B is a polynomial:Yes
