## anonymous one year ago .

1. anonymous

i would factor it, then make a table hen graph iy

2. UsukiDoll

almost.... you need to factor more

3. UsukiDoll

ok... you have a perfect square in the form of $(a^2-b^2) = (a+b)(a-b)$

4. UsukiDoll

$(x^2-4)$ is a perfect square.. what is the square root of x^2 and what is the square root of 4

5. UsukiDoll

no.

6. Zale101

|dw:1434948176809:dw|

7. UsukiDoll

a perfect square is the product of a rational number multiplied by itself. the product of a polynomial multiplied by itself.

8. UsukiDoll

A perfect square is a number that can be expressed as the product of two equal integers.

9. UsukiDoll

what are you doing?

10. Zale101

a is squared and so does x b is squared but 4 is the square of what number?

11. UsukiDoll

$f(x) = x^3 + 4x^2 - x - 4$ factor by grouping which you did and that's fine you got to $(x^2-4)(x+1)$ but you need to factor more..

12. Zale101

$$\Large (a^2-b^2)=(a+b)(a-b)$$ $$\Large (x^2-4)=(x^2-2^2)$$ clear?

13. UsukiDoll

something's wrong here.

14. UsukiDoll

factor my grouping (at least when I did it) had something else as a perfect square

15. UsukiDoll

$f(x) = x^3 + 4x^2 - x - 4 \rightarrow x^2(x+4)-1(x+4)$

16. UsukiDoll

$(x+4)(x^2-1)$

17. UsukiDoll

you shouldn't rearrange the terms.. -_- that's why you had a different answer.

18. UsukiDoll

second line is where everything got messed up x^3+x-4x^2-4 x(x^2+1)-4(x^2+1) you have an imaginary number case

19. UsukiDoll

Leave the function alone! *FIRST STEP* Second step use factor by grouping (two pairs!) first and second term has a common factor.. third and fourth term has a common factor

20. UsukiDoll

$f(x) = x^3 + 4x^2 - x - 4$ look at the first two terms.. what do they have in common?

21. UsukiDoll

ok .. we have four terms x^3 <- 1st term 4x^2 - 2nd term -x <- 3rd term -4 < - 4th term focus on the first and second only what do they have in common?

22. UsukiDoll

yes... how many x's though?

23. UsukiDoll

$x^3-4x^2 => (x)(x)(x)-4(x)(x)$

24. UsukiDoll

how many x's can I take out?

25. UsukiDoll

WHAT! I have three x's and I have 2 x's

26. UsukiDoll

-x-4 now what can I take out? =_=

27. UsukiDoll

what can I yank out to make sure I have (x+4) ?

28. UsukiDoll

I have -x-4 I want x+4 what do I need to yank out?