Question

explain the grouping method of factoring to me please? can you also give me an example of when it would be used over the other methods of factoring? thanks!

Answer 1

the grouping method is useful for factoring trinomials
eg

factor x^2 - 3x - 18

we can write the middle terms as +3x - 6x (note 3 *- 6 = -18):

= x^2 + 3x -6x - 18

= x(x + 3) -6 (x + 3)

take out the common factor x+3 to give

(x + 3)(x - 6)

Answer 2

im not sure i understand, what is the first step to factoring this trinomial?

Answer 3

another name for this polynomial is a quadratic - note it has a term in x^2 . in x and a number
these can factor to the form (x + a)(x + b)
- if we expand this we get x^2 + ax + bx + ab
so the last term the number = ab and the middle term in x will have the coefficient a+b
so if we consider
x^2 - 3x - 18 we need to find the values of a and b and we knoe that ab = -18 and a + b = -3
2 numbers come to mind -6 and +3
so we write
x^2 -6x + 3x - 18
the we look to factor this by grouping
what are the 2 groups - we need to factor them and to get a common factor in the brackets:-
by observation we see they are x^2 + 3x and -6x - 18
x^2 + 3x - 6x - 18
= x(x + 3) - 6( x + 3)

Answer 4

thanks man

Answer 5

yw