Some Polynomials Cannot be Factored
Sometimes there is no way to rearrange or group that produces common factors. A polynomial that cannot be factored down to one term is said to be unfactorable.
Factor: y2 12y 32
Practice factoring: y2 12y 32.
Factor: ax 3x 3b 3y
A polynomial with four terms can be factored by grouping when there is no factor common to all four terms. The procedure is demonstrated and the process checked using the FOIL method and applying the commutative law.
Factor: d2 - 13d 30
The terms in a quadratic trinomial can be positive or negative. A quadratic trinomial in which the middle term is negative is factored.
Fractions Raised to a Power
Simplifying expressions in which a fraction is raised to a power.
Factor: x2 5xy 4y2
Factoring a trinomial with two different variables: x2 5xy 4y2.
Factor: 3x2 14x 8
Factoring a quadratic trinomial with a leading coefficient greater than one that has no greatest common factor. In general, whenever factoring a quadratic trinomial with a coefficient greater than one look for a pair of numbers in which the sum is e...
Multiplying a Monomial by a Trinomial
Solving a practical problem algebraically using multiplication of a monomial by a trinomial.
Adding More Complex Expressions
Demonstration of adding terms in a complex algebraic expression and a practical problem demonstrating application of this skill in the real world.
Adding Rational Numbers with Different Denominators
In order to add or subtract rational expressions with different denominators, the least common denominator must be found and the fractions rewritten with the same denominator.