Factor: a2 12a 27
Demonstration of a shortcut that can be used to factor a quadratic trinomial with a leading coefficient of 1.
Factor: a2 - ac - ab bc
When grouping terms, the goal is to end up with an expression that is equal to the original polynomial. Close attention to the signs is necessary to ensure a correct outcome. Remember that a minus sign in front of parent..
Factor: ab – 2a 3b - 6
The polynomial expression ab — 2a 3b - 6 is factored by grouping and the solution checked. The factors check when the terms and their signs are the same as those in the original polynomial.
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: ax - x - 5a 5
Practice with factoring involving minus signs: ax - x - 5a 5.
Factor: b2 9b 20
A quadratic trinomial with a leading coefficient of 1 is factored, producing a four-term polynomial. The factor is then checked by multiplying using the FOIL method.
Factor: c2 - cd c - d
Although a factor of one is not usually written in an expression, it sometimes helps to write it down in order to remember that it is part of the factor and can be used, as demonstrated in the example c2 - cd c - d.
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.
Factor: x2 5x - 24
A quadratic trinomial in which the last term is negative is factored.
Factor: x2 5xy 4y2
Factoring a trinomial with two different variables: x2 5xy 4y2.