Answer:
See below
Step-by-step explanation:
Factoring a trinomial of the form ax^2 + bx + c.
I think this is best understood by studying some examples.
<u>Examples</u>:-
Trinomials where a = 1:-
Factor x^2 + 3x + 2 (Its not usually written as 1x^2).
We need 2 numbers whose product = the last term (2) and whose sum = 3 ( the coefficient of x).
They are 1 and 2. The factors are 2 binomials as follows:-
(x + 1)(x + 2) (answer)
2. Factor x^2 - x - 6
We need 2 numbers whose product is -6 and whose sum = -1 ( its -1 because we can write the middle term - x as -1x ).
The 2 numbers are -3 and 2 , so the factors are:-
(x - 3)(x + 2) (answer)
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Now we come to trinomials that have a value of a > 1:-
Example 1.
Factor 2x^2 + 5x + 2
We can use the 'ac' method.
First multiply 'a' by 'c' ( from ax^2 + bx + c):-
2 * 2 = 4.
Now we need 2 numbers whose product is 4 and whose sum is the coefficient of x, (= 5). These are
4 and 1.
Now we rewrite the 5x in the trinomial as 4x + x :-
2x^2 + 5x + 2
= 2x^2 + 4x + x + 2
Next Factor this by grouping:-
= 2x(x + 2) + 1(x + 2)
Note that x + 2 is common so w have the factors:-
(2x + 1)(x + 2) (answer).
Example 2.
Factor 3x^2 - 10x - 8
3 * -8 = -24
The 2 required numbers are -12 and 2 because -12*2 = -24 and -12 + 2 = -10. So we write:-
3x^2 - 12x + 2x - 8
= 3x(x - 4) + 2(x - 4)
= (3x + 2)(x - 4) (answer).
Hope this helps.
My advice is Practice as much as you can.
