We factor Polynomials using synthetic substitution, grouping, or by using Polynomial Identities such as the sum and difference of cubes.
Sample Math Problems
Synthetic Substitution:
Synthetic Substitution can help us to determine whether a given binomial x-a is a factor of the polynomial, because we can use it to see if P(a)=0.
For example:
Let’s try x+3 for
P(x)=-2x+5;
First x-a = x+3a => -3
Now we find P(-3). In synthetic substitution, we take a and the coefficients and constants of a polynomial. Bring down the first coefficient. From there, we multiply and add each column.
Thus we get P(x)=47 in the last column.
Looking at this, we can tell that x+3 is not a factor of P(x).
Now let’s see what happens when a binomial is a factor:
Grouping:
Some polynomials can be factored by grouping together terms with common factors. This usually happens if a difference of squares is a factor of the polynomial.
Sum and Difference of Cube
