Solved example of synthetic division of polynomials
We can factor the polynomial $x^4+x^3-6x^2-4x+8$ using synthetic division (Ruffini's rule). We search for a root in the factors of the constant term $8$ and we found that $1$ is a root of the polynomial
Let's divide the polynomial by $x-1$ using synthetic division. First, write the coefficients of the terms of the numerator in descending order. Then, take the first coefficient $1$ and multiply by the factor $1$. Add the result to the second coefficient and then multiply this by $1$ and so on
In the last row of the division appear the new coefficients, with remainder equals zero. Now, rewrite the polynomial (a degree less) with the new coefficients, and multiplied by the factor $x-1$
We can factor the polynomial $\left(x^{3}+2x^{2}-4x-8\right)$ using synthetic division (Ruffini's rule). We search for a root in the factors of the constant term $-8$ and we found that $2$ is a root of the polynomial
Let's divide the polynomial by $x-2$ using synthetic division. First, write the coefficients of the terms of the numerator in descending order. Then, take the first coefficient $1$ and multiply by the factor $2$. Add the result to the second coefficient and then multiply this by $2$ and so on
In the last row of the division appear the new coefficients, with remainder equals zero. Now, rewrite the polynomial (a degree less) with the new coefficients, and multiplied by the factor $x-2$
The trinomial $\left(x^{2}+4x+4\right)$ is perfect square, because it's discriminant is equal to zero
Using the perfect square trinomial formula
Factoring the perfect square trinomial
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