What is the quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1)?
Solution:
Given: p(x) and g(x) are the given two polynomials.
Let p(x) = x³ + 3x² + 5x + 3 ; g(x) = x + 1.
To find the quotient we need to perform p(x) ÷ g(x)
We will use the long division of polynomials to find the quotient of the polynomial.
Thus x² + 2x + 3 is the quotient when p(x) divided by g(x).
Divisibility Check:
Dividend = Divisor × quotient + remainder
x³ + 3x² + 5x + 3 = (x + 1) × (x² + 2x + 3) + 0
x³ + 3x² + 5x + 3 = (x³ + 2x² + 3x + x² + 2x + 3) + 0
x³ + 3x² + 5x + 3 = x³ + 3x² + 5x + 3
LHS = RHS
Hence by using the long division method, the quotient of the polynomial p(x) = x³ + 3x² + 5x + 3 when divided by the polynomial g(x) = x + 1 is x² + 2x + 3.
What is the quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1)?
Summary:
The quotient when x³ + 3x² + 5x + 3 is divided by x + 1 is x² + 2x + 3.