The quotient of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3) is (x + 2) after factorization of the polynomial.
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial:
= x³ + 6x² + 11x + 6
The above polynomial is divided by x² + 4x + 3
= (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3)
To find the quotient:
[tex]\rm =\dfrac{\left(x+1\right)\left(x+2\right)\left(x+3\right)}{x^2+4x+3}[/tex]
[tex]\rm =\dfrac{\left(x+1\right)\left(x+2\right)\left(x+3\right)}{\left(x+1\right)\left(x+3\right)}[/tex]
[tex]\rm =x+2[/tex]
Thus, the quotient of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3) is (x + 2) after factorization of the polynomial.
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