factoring trinomials?

Question

Could u please explain in detail how to factor the following this problem and how you got the answer like what are the steps thx and this is an example given although i do not know how the answer was got 2x^2 - 5x -3= (2x +1 ) (x- 3)



1.) 3x^2 + 10x - 8

Answer 1

First you put two sets of parentheses. Then you figure out what times what would bethe first term: 3x^2. Guess that is it 3x times 1x and write 3x in the beginning of the first set of ( ) and 1x in the second:

(3x.......)(1x........)

The look at the last term: -8 You need two numbers that multiply to be negative 8, so one is positive and the other negative. You must guess them and try. Guess +2 and -4 Put these after the 3x and the 1x:

(3x + 2)(1x - 4)

Now multiply the 3x by the -4, and the 1x by the +2 then combine:

-12x + 2x = -10x

Now you wanted + 10x not -10x so switch the signs:

(3x - 2)(x + 4)

If the answer -10x was not even the right number, you'd go back and switch the 2 and 4. If that still dodn't work you'd try +8 and -1.

There can be a lot of guess and check at first til you get good at it.

Answer 2

You can take
3x^2 + 10x - 8
and expand it to
3x^2 + (3A)x + Bx - 8
so that you get the two factors (3x + B) (x + A).

So you're looking for two numbers A & B such that 3*A + B = 10 and A*B = 8.

By inspection, you should be able to try 4 and -2 since, 3*4+B=12-2=10 and 4*-2=-8.

SO THE FACTORS ARE (3x - 2)(x + 4) = 3x^2 + 10x - 8.
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If you can't do it by inspection you have to solve the quadratic, x1,x2 = ((-b +- sqrt(b^2 - 4ac)) / 2a) for ax^2 + bx + c and then the two factors are (3*x - 3*x1)(x - x2). It doesn't matter which is used as x1 or x2, but it looks better if one of them is fractional thirds and the other is an integer, to use the fraction as x1.

x1,x2 = ((-10 +- sqrt(10^2 + 4*3*8)) / (2*3)) = ((-10 +- sqrt(100 + 96)) / 6) = ((-10 +- 14) / 6) = +4/6,-24/6 = 2/3, -4.

(3x - 3(2/3))(x - 4) = (3x - 2)(x + 4) = (3x^2 + 10x - 8)

Answer 3

3x^2+10x-8
=(3x-2)(x+4)

(3*4)+(1*-2)=10
-2*4=-8