Factoring quadratic polynomials

[lioni]

ok so i have tried to solve this problem many many ways and i still cant seem to come up with correct answer.

the problem is 2x^2+7x-15. It is currently in the general form and needs to be converted into the factored form.

It seems like I cannot get the values that add up to 7 and to multiply to -15.

I have used the box method. and it really isnt working :?

 

[Denis]

the problem is 2x^2+7x-15. It is currently in the general form and needs to be converted into the factored form.
It seems like I cannot get the values that add up to 7 and to multiply to -15.

That "trick" only works if 1st term is x^2.
Use the quadratic formula.

 

[lioni]

the quadratic formula answers didnt come out to be correct either. i got 1.5 and -5 for x's
so when i remultiplied them i didnt get the correct answer

 

[Aladdin]

Yep, the solutions are : 1.5 & -5

To factorise it , (a)(x-1.5)(x-(-5)

which leads to , 2(x-1.5)(x+5)

(x-1.5)(2x+10)

 

[fasteddie65]

2x^2 + 7x - 15

Try the technique called the Product-Sum Method.

Multiply 2 and -15. -30 is the product.

Find factors of -30 whose sum is 7.

List the factors of -30: -1, 30; 1, -30; 2, -15; -2, 15; -3, 10; 3, -10; 5, -6; -5, 6.

The pair that has the right sum is -3 and 10.

Rewrite the trinomial as a four term polynomial, using the numbers -3 and 10 replace the 7.

2x^2 - 3x + 10x - 15

Regroup into two binomials: (2x^2 - 3x) + (10x - 15)

Factor each binomial: x(2x - 3) + 5(2x - 3)

Take out the common binomial factor: 2x - 3

(2x - 3)(x + 5)

The method works best if you can arrange it so that the third term in the four terms is positive. If not, it gets a little bit trickier.

If a trinomial can be factored, this method will work every time.

 

[stapel]

the problem is 2x^2+7x-15. It is currently in the general form and needs to be converted into the factored form.

It seems like I cannot get the values that add up to 7 and to multiply to -15.

I have used the box method.

To learn how to use the "box" method, try here. You will note that the first step is to find factors of "ac" (not just "c") that add to "b". So you're actually looking for factors of -30 that are seven units apart.

(Hint: +10 and -3.) :wink: