using ploynomial division rewrite the equation as a transformation
To rewrite an equation using polynomial division, you can follow these steps:
1. Write the equation as a division problem, with the numerator being the polynomial you want to divide and the denominator being the divisor polynomial.
2. Perform long division on the polynomials, dividing the terms with the highest degrees first.
3. Write the quotient as a transformed equation.
Here's an example to illustrate the process:
Let's say we have the equation: x^3 + 4x^2 + 3x + 2 = (x + 1)(x^2 + 3).
Step 1: Write the equation as a division problem:
(x^3 + 4x^2 + 3x + 2) ÷ (x + 1)
Step 2: Perform long division:
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x + 1 | x^3 + 4x^2 + 3x + 2
- (x^3 + x^2) <= Divide x^3 by x
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3x^2 + 3x
- (3x^2 + 3x) <= Divide 3x^2 by x
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0
Step 3: Write the quotient as a transformed equation:
The quotient is 0, so we can rewrite the original equation as:
x^3 + 4x^2 + 3x + 2 = (x + 1)(x^2 + 3)
Therefore, we transformed the equation using polynomial division.
Note: Polynomial division is also useful to find the remainder, if any, when dividing polynomials.