Answer:
[tex]x^2-x-12=(x-4)(x+3)[/tex]
Step-by-step explanation:
Factoring a Trinomial
A trinomial is expressed in the form
[tex]ax^2+bx+c[/tex]
Where a,b, and c are real constants.
Some trinomials can be factored as the product of binomials with real coefficients, while others cannot.
If possible, factoring can be done in several ways:
- Factoring out the GCF.
- The sum-product pattern (by inspection).
- The grouping method.
- The perfect square trinomial pattern.
- The difference of squares pattern.
- Knowing the roots
Each method is most likely applicable under certain circumstances. When the polynomial has a leading coefficient of a=1, the sum-product pattern is the fastest and easiest option.
We have the polynomial
[tex]x^2-x-12[/tex]
Here: a=1, b=-1, c=-12
The sum-product method needs us to find two numbers which sum is -1 and product is -12. Those numbers can be found by inspection by combining two divisors of 12, say 1 and 12, 2 and 6, or 3 and 4.
Only one of those pairs can be combined to produce a sum or subtraction equal to -1: Those numbers are -4 and 3. Thus the factorization is:
[tex]\mathbf{x^2-x-12=(x-4)(x+3)}[/tex]
