can anyone help me with factoring trinomials?

Question

i'm not asking for the answers. i just need some help remembering the basic concept of ax^2 + bx + c or whatever :) i forgot everything over the summer.

Answer 1

You can use the AC method. This is where you multiply A*C (remember to include the signs.) Then you look for a pair of numbers that multiply to form this number (AC) but add to give you the value B in the middle.

Now, use those values to rewrite the middle term, Bx. Then factor by grouping (group the first 2 and then the last 2 terms) and you're done!

Ex. 6x^2 - 11x - 10
Multiply 6 * (-10) = -60
Now find 2 numbers that multiply to give -60 but add up to -11. How about 4 and -15?
Rewrite the middle term (remember to include the "x")using these numbers:
6x^2 + 4x -15x -10 <----- see how the 2 middle terms combine to give you -11x?

Now group the first 2 terms, (you can factor out 2x) and group the last 2 terms, (you can factor out a -5.)

2x(3x + 2) - 5(3x + 2) <----- be careful with your signs here!

See how the 2 binomials in parentheses match? Now you can factor out this common term to get:
(3x+2)(2x - 5)

Voila! Remember you can always check your factoring by applying FOIL to get back to the original polynomial.

good luck!

Answer 2

ax^2 + bx + c
The best approach is to 1st compute b^2-4ac.
If b2-4ac = 0 Then the factors are (x+b/2a)^2.
If b^2-4ac<0, then there are no real factors.
If b^2-4ac > 0, and if b^2-4ac is a perfect square, then the function has real factors and real roots.
If b^2-4ac >0 but is not a perfect square, then the roots are irrational and the factors will be irrational.

Look at an example:
x^2 +2x - 255
b^2-4ac = 4+1020 = 1024 = 32^2 , a perfect square. So we know the function can be factored.
So roots will be (-2 +/- 32)2 = -17 and 15
So the factors are (x+17(x-15) = x^2 +2x -255

Answer 3

It's not factorable (otherwise known as a prime trinomial) simply because of the negative. if either the 42 or the 26n were positive, it would have worked out

Answer 4

ax^2 + bx + c
= a[x+(b+√(b^2-4ac))/(2a)] [x+(b-√(b^2-4ac))/(2a)]
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Any quadratic function can be factored with the quadratic formula.