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nexus9112 [7]
2 years ago
9

The quotient of (x4 â€"" 3x2 4x â€"" 3) and a polynomial is (x2 x â€"" 3). What is the polynomial? x4 â€"" 2x2 5x â€"" 6 x2 â€""

x 1 x6 x5 â€"" 6x4 x3 10x2 â€"" 15x 9 x4 â€"" 4x2 3x.
Mathematics
1 answer:
Sever21 [200]2 years ago
8 0

The quotient of polynomials is the division of the polynomials

The polynomial is x^6 + x^5 -6x^4 +x^3 +10x^2-15x +9

Represent the polynomial with P.

So, the quotient is represented as:

\frac P{x^4 -3x^2 + 4x - 3} = x^2 + x -3

Make P the subject

P = (x^4 -3x^2 + 4x - 3)( x^2 + x -3)

Expand the expression on the right-hand side of the equation

P =x^4(x^2 + x -3) -3x^2(x^2 + x -3) + 4x(x^2 + x -3) - 3(x^2 + x -3)

Further, expand

P =x^6 + x^5 -3x^4 -3x^4 - 3x^3 +9x^2 + 4x^3 + 4x^2 -12x - 3x^2 - 3x +9

Collect like terms

P =x^6 + x^5 -3x^4 -3x^4 - 3x^3+ 4x^3 +9x^2  + 4x^2  - 3x^2-12x - 3x +9

Evaluate like terms

P =x^6 + x^5 -6x^4 +x^3 +10x^2-15x +9

Hence, the polynomial is x^6 + x^5 -6x^4 +x^3 +10x^2-15x +9

Read more about quotient of polynomials at:

brainly.com/question/9949019

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