factoring----- factor 2x^2+3x-9?

Question

can some one explain step by step how to factor 2x^2+3x-9

(2x^2 i mean this to be 2x squared)

Answer 1

First: multiply the 1st and 3rd coefficient to get "-18". Find two numbers that give you "-18" when multiplied and "3" when added/subtracted. The numbers are: "6" and "-3".....

Sec: rewrite the equation including the new middle coefficients....

2x^2 + 6x - 3x - 9

*When you have 4 terms - group "like" terms and factor....

(2x^2 + 6x) - (3x - 9)

2x(x + 3) - 3(x + 3)

Third: you have the inner term repeated twice, just combine one of inner terms with the outer terms...

(x + 3)(2x - 3)

Answer 2

The easiest way may be the most tedious way.

Let's start by looking at this backwards.

If I wanted to multiply (2x + 3)(x - 3), I would use the FOIL method. I prefer to think of it as double distribution. I would multiply the 2x by everything in the second set of parenthesis, then I woul multiply the +3 by everything in the second set of parenthesis.

Therefore:
(2x)(x) = 2x^2
(2x)(+3) = 6x
You're done with the 2x, so move to the second term, the -3
(-3)(x) = -3x
(-3)(3) = 9.

Combining like terms now gives you 2x^2 + 3x - 9.
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Now that we have this background, we can work backwards to answer your question.

STEP 1: Notice that if I want to factor 2x^2 + 3x - 9, I want to break it into two sets of parenthesis, such as (____x + ____)(____x + _____)

STEP 2: Now look at the first term, the 2x^2. Where does that term come from? It comes from multiplying the first terms in each set of parenthesis, or the x's. It has nothing to do with the numbers after them. So my first question is "What two terms do I muliply to get 2x^2?" Fortunately, there is only one choice. It has to be 2x and x.

Therefore, I have (2x + ____)(x + ____)

STEP 3: Now that I have those two terms, I look back at 2x^2 + 3x - 9. Notice how the last term is -9? Where does that come from? It is found by multiplying the second term in each set of the parenthesis. It has nothing to do with the x's from before.

So I list the factors of -9, which are:
-1 and 9
1 and -9
-3 and 3.
3 and -3
If this equation is factorable, then one of these four combinations is the solution.

STEP 4: This is more of a trial and error. You plug in your solutions from step 3 into your possible solution and see if it works. (The first and last should automatically work, but you may want to multiply the whole thing out just in case.)

(2x + 1)(x - 9) = 2x^2 -18x + 1x -9 = 2x^2 -17x - 9...not the solution.

(2x - 1)(x + 9) = 2x^2 +18x - 1x -9 = 2x^2 +17x - 9...not the solution.

(2x - 3)(x + 3) = 2x^2 + 6x -3x - 9 = 2x^2 +3x +9. so this must be the solution.

Hope that helps.

Answer 3

The answer is (2x - 3)(x + 3).

To get there, you first assume that all the coefficients are whole numbers.
To obtain 2x² , the only possibility then is to multiply 2x by x .
To obtain -9 , there are six possibilities:
+3 multiplied by -3
-3 multiplied by +3
+9 multiplied by -1
-9 multiplied by +1
+1 multiplied by -9
-1 multiplied by +9
It's then a matter of trial and error:
(2x + 3)(x - 3) which = 2x² - 3x - 9
(2x - 3)(x + 3) which = 2x² + 3x - 9
(2x + 9)(x - 1) which = 2x² + 7x - 9
(2x - 9)(x + 1) which = 2x² - 7x - 9
(2x + 1)(x - 9) which = 2x² - 16x - 9
(2x - 1)(x + 9) which = 2x² + 16x - 9
Clearly, only the second one gives the desired result.

P.S. To obtain the 'squared' sign, use Alt-253.

Answer 4

You need to know the factors of both 2 and 9
1,2 and 1,3,9
The 1 and 2 is easy

(2x + ) (x - )

Now you need to stick in the factors of 9 that create the middle term of +3. Looks like I need to reverse the signs.
(2x - 3)(x+3)

Answer 5

-35 x^4 y^9.... There is nothing to factor here... x^3 - 2x^2 - 3x + 6 = (x^2 - 3)(x -2) 9z^2 + 6z - 8 = (3z-2)(3z+4) 5x^3 + 5x^2 - 60x = 5x(x^2 + x -12) = 5x(x-3)(x+4) 12m^8 + 28m^6 + 16m^4 = 4m^4 (3m^4 + 7m^2 + 4) = 4m^4 (3m^2 + 1)(m^2 +4)

Answer 6

list the factor of 2 and 9

1 -3
2 3
2x^2+3x-9
cross multiply
(2x-3)(x+3)

Answer 7

2x^2+3x-9
(2x-3)(x+3)

Answer 8

the answer is ;
(2x - 3)(x + 3)....ans.

check;
(2x - 3)(x + 3)....
2x^2 + 6x-3x-9 = 2x^2 + 3x-9...............

Answer 9

2x^2+3x-9
(2x+3)(x-3)=answer
2x^2+6x-3x-9

I hope this helps

Answer 10

1. solve 2x^2 which is 2xtimes2x=4x
2. then combine like terms, 4x+3x=7x
3. then you write out the answer 7x-9
-michelle