## alexeis_nicole 3 years ago how would i factor 8x^2 + 2x -21

1. sasogeek

multiply the coefficient of the x^2 term by the constant and find 2 factors of the result that when you add or subtract will give you the x coefficient, replace the x coefficient with the two factors in a way that when you subtract or add them, you'll get the x coefficient. you'll get 4 terms. take the first two terms and factor them, take the last two terms and factor them. you're done. if you didn't understand what i've just written, read it carefully again, take your time, and solve it.

2. King

You can use the quadratic equation formula (-b +or-sqrt(b^2-4ac))/2a here a,b,c are the coefficients ax^2+bx+c

3. King

understood? @alexeis_nicole

4. alexeis_nicole

yep.. i got 24 and 26... :S ?

5. alexeis_nicole

I MEAN ... 1.5 AND -1.75?

6. agentx5

Quadratic Formula in an easier-to-read form: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ Binomials will be written as (where a, b, and c are numerical constants) $ax^2 + bx + c$ You can always check your factorization by multiplying it back together to get the original expanded form (what you have initially here).

7. agentx5

1.5 and -1.75 are correct, but put them in fraction form and you'll have a huge hint ;-)

8. alexeis_nicole

3/2 and -7/4 ?

9. agentx5

Huge hint: $\frac {numerator}{demominator} = \frac {c}{a}$

10. agentx5

(ax+c)(ax+c) (but different a's and c's, call them a1 & c1 and a2 & c2 if you want)

11. agentx5

Here's one of the two, so you're not getting confused: -7/4 --> (4x+7)

12. agentx5

Here's how to check, solve this: $4x+7 = 0$

13. alexeis_nicole

OH !!!!! (2x-3) (4x+7)

14. agentx5

You got it!

15. agentx5

Do you see why the -/+ sign switches?

16. agentx5

So here's the next step they'll probably introduce you to later, they'll ask you to solve this: $8x^2 + 2x -21 = (2x-3)(4x+7) = 0$

17. alexeis_nicole

uhm,.... lol