Introduction to Factoring Quadratic Trinomials
A quadratic trinomial is a polynomial with three terms. In two of the terms the same variable appears, one that is raised to the second power and the other with an exponent of one. The third term in a quadratic trinomial is a constant. To factor a q...
Factor: 2k2 - 18k - 72
Factoring a quadratic trinomial with a leading coefficient greater than one.
Not All Quadratic Trinomials Can Be Factored
A quadratic trinomial that cannot be factored is presented and explained.
Multiplying by the Least Common Denominator to Get a Quadratic Equation
The steps involved in solving an equation by multiplying by the least common denominator to get a quadratic equation and checking the solution are detailed.
Solving an Equation with the Least Common Denominator: Practice Problem
A problem is presented to practice solving an equation using the least common denominator to get a quadratic equation.
Practical Problem: Machines Working at Different Speeds
The procedure for developing an equation to solve a practical work problem involving machines working at different speeds is detailed. The unknown is identified and an equation is written, solved, and checked.
Practical Problem: Runners' Rate of Speed
The rate, time, and distance formula is used to solve a practical problem involving runners' rate of speed.
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.
Terms Can Be Grouped Differently
There is often more than one way to group a polynomial expression for factoring. The commutative law can be applied to rearrange the terms into different factorable groups.