The quotient of polynomials is the division of the polynomials
The polynomial is [tex]x^6 + x^5 -6x^4 +x^3 +10x^2-15x +9[/tex]
Represent the polynomial with P.
So, the quotient is represented as:
[tex]\frac P{x^4 -3x^2 + 4x - 3} = x^2 + x -3[/tex]
Make P the subject
[tex]P = (x^4 -3x^2 + 4x - 3)( x^2 + x -3)[/tex]
Expand the expression on the right-hand side of the equation
[tex]P =x^4(x^2 + x -3) -3x^2(x^2 + x -3) + 4x(x^2 + x -3) - 3(x^2 + x -3)[/tex]
Further, expand
[tex]P =x^6 + x^5 -3x^4 -3x^4 - 3x^3 +9x^2 + 4x^3 + 4x^2 -12x - 3x^2 - 3x +9[/tex]
Collect like terms
[tex]P =x^6 + x^5 -3x^4 -3x^4 - 3x^3+ 4x^3 +9x^2 + 4x^2 - 3x^2-12x - 3x +9[/tex]
Evaluate like terms
[tex]P =x^6 + x^5 -6x^4 +x^3 +10x^2-15x +9[/tex]
Hence, the polynomial is [tex]x^6 + x^5 -6x^4 +x^3 +10x^2-15x +9[/tex]
Read more about quotient of polynomials at:
https://brainly.com/question/9949019
