Question

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.

Answer 1

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