AI polynomial division equation solver is powered by MathCrave AI algorithms to:
Simplifies polynomial divisions
Divides algebraic expressions with polynomial divisions
Factorizes expression using the factor theorem
Uses the remainder theorem to factorize algebraic expressions
Example Divide 3x^3 + x^2 + 3x + 5 by x + 1
To solve the polynomial division of 3x^3 + x^2 + 3x + 5 by x + 1, follow the steps below:
Step 1: Write the dividend and divisor in descending order of exponents:
3x^3 + x^2 + 3x + 5 ÷ (x + 1)
Step 2: Divide the first term of the dividend (3x^3) by the first term of the divisor (x):
(3x^3 ÷ x) = 3x^2
Step 3: Multiply the quotient obtained in Step 2 by the divisor (x + 1):
3x^2 (x + 1) = 3x^3 + 3x^2
Step 4: Subtract the result obtained in Step 3 from the dividend:
(3x^3 + x^2 + 3x + 5) - (3x^3 + 3x^2) = -2x^2 + 3x + 5
Step 5: Bring down the next term of the dividend (-2x^2) and repeat Steps 2 to 4:
(-2x^2 ÷ x) = -2x
-2x (x + 1) = -2x^2 - 2x
(-2x^2 + 3x + 5) - (-2x^2 - 2x) = 5x + 5
Step 6: Repeat Steps 2 to 4 with the remaining terms:
(5x ÷ x) = 5
5 * (x + 1) = 5x + 5
(5x + 5) - (5x + 5) = 0
Step 7: The quotient is obtained by adding all the quotients from each step:
Quotient = 3x^2 - 2x + 5
A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, multiplication, and non-negative integer exponents.
Polynomial division is the process of dividing a polynomial by another polynomial. It is similar to long division, where the dividend (the polynomial being divided) is divided by the divisor (the polynomial dividing the dividend), and the quotient and remainder are obtained.
