## anonymous one year ago .

1. anonymous

split the middle term, do you know how to do that?

2. anonymous

kind of but could you please walk me through the steps

3. anonymous

I'll try when you split the middle term of a quadratic polynomial $p(x)=ax^2+bx+c$ you are looking to split b into two numbers say, f and g such that $b=f+g$ and $f \times g =a \times c$ Do you understand this?

4. anonymous

yes

5. anonymous

Ok now calculate $a \times c$ for the polynomial u r given

6. anonymous

|dw:1438524585865:dw|

7. anonymous

okay keep going i understand

8. anonymous

can u find the product of a and c for me

9. anonymous

-12

10. anonymous

ok good, now what is your b?

11. anonymous

-4

12. anonymous

great, now can you think of two numbers u can split b(that is -4 in this case) into, such that the product of those numbers will equal -12 and adding those numbers will give u back -4

13. anonymous

-6 and 2

14. anonymous

good job!! now just split b and work it out as $12x^2+(-6+2)x-1=12x^2-6x+2x-1$

15. anonymous

factorize first 2 terms together and last 2 terms together

16. anonymous

what two terms

17. anonymous

|dw:1438524844892:dw|

18. anonymous

take out as much factors out as u can from the first 2 terms

19. anonymous

|dw:1438524921185:dw| What does that say?

20. anonymous

it's 6x, for the first 2 terms what can u take out??what is common in 12x^2 and -6x ??

21. anonymous

6x(2x-1)

22. anonymous

good, now so now we have $6x(2x-1)+(2x-1)$ Now we have two terms, you can take 2x-1 out, what are you left with?

23. anonymous

6x

24. anonymous

nope, you are missing something!! $(2x-1)(6x+??)$

25. anonymous

1?

26. anonymous

yep! and there you have your factors, nice and clean $(2x-1)(6x+1)$ Just to verify, let's open these up $(2x \times 6x)+( -1 \times 6x)+(2x \times 1)+(-1 \times 1)=12x^2-6x+2x-1=12x^2-4x-1$

27. anonymous

12x^2-4x-1

28. anonymous

Thanks