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Factoring Trinomials – Basics
To factor trinomials, knowledge of the greatest common factor (GCF) is required, as usual for factoring of any type. First of all, the biggest common factor for the three terms is knowing and if there is a PGCF, it is extracted from each of the three terms of the trinomial.
Once the PGCF is removed (if there is one present in the given trinomial), then if the trinomial is a quadratic trinomial of type, “ax² + bx + c” there is then a special technique to factorize this type of polynomials. If the polynomial after removing the gcf is a degree polynomial, then the given form of the solution is the answer for the trinomial factorization.
Now, the quadratic trinomial is a degree two trinomial as given by the standard quadratic trinomial “ax² + bx +c”, where “a”, “b”, and “c” are the integers. If the value of “a” (the coefficient of x²) is the number “1”, then the above quadratic trinomial can be written as “x² + bx + c” and depending on the signs of “b” and “c”, the following kinds of expressions can be formed.
1.x² + 3x + 2
The polynomial above is a standard quadratic trinomial, having the value of “a” equal to “1”, the value of “b” equal to “+3” and the value of “c” equal to “+2”.
To factor it, we need to find the factors of the number “2” (“c” in the standard trinomial) that add up to the number “3” (“b” in the standard trinomial).
Now number 2 has only two factors, 1 and 2 itself and they also add up to 3. Hence, we have found the solution to our factoring problem. The numbers required to factor the trinomial are “1” and “2” because they multiply by “2” (value of “c” for the standard polynomial) and they add up to “3” (which is the value of “b” ).
The factors can be written as shown below:
x² + 3x + 2
= (x+1) (x+2)
Now if we “THROUGH” the answer (x+1) (x+2), we recover the original trinomial, which confirms that our factors are correct. If by multiplying the factors you do not get the same polynomial that you factored, this is an indication of bad factorization. In this case, proofread your work to find the error and correct it.
More examples of factoring are given below for you to practice.
2. t² + 6t + 9
3.x² + 15x + 26
4. a² – 10x + 16
5. x² – x – 12
Try the examples above, if you want the solutions to the above factoring problems, email me (my email is on my profile page) and I’ll send you the detailed solutions in the 48 hours.
Sincerely, Manjit Singh
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