## anonymous one year ago Let f(x) = 4x^2 + x + 1 and g(x) = x^2 – 2. Find g(f(x)). Show each step of your work.

1. anonymous

@phi @pooja195 @triciaal

2. anonymous

3. triciaal

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4. anonymous

What I have so far: Original: f(x) = 4x^2 + x + 1; g(x) = x^2 – 2 Combine: (4x^2 + x + 1)^2 - 2

5. triciaal

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6. anonymous

16x^4 + x^2 + 1?

7. triciaal

no (a + b + c)^2 = (a + b + c)(a + b + c) not enough terms it might be easier to complete the square

8. anonymous

Whatever is easier

9. triciaal

do you have choices?

10. anonymous

No, this is written.

11. triciaal

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12. triciaal

16x^4 + 8x^3 + 9x^2 + 2x -1

13. triciaal

if might be enough to show the substitution and get the right expression for g(f(x)) or to get the above with the expansion

14. anonymous

Wow, okay, so... ((2x)^2 + x + 1)^2 - 2 What's the second row?

15. triciaal

do you know how to use the distributive property? some people use FOIL to remember but that is with 2 terms here we have 3 terms inside you need to multiply each term

16. triciaal

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17. anonymous

Could you type out the second row please?

18. triciaal

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19. triciaal

simplify this then subtract 2

20. anonymous

((2x)^2 + x + 1)^2 - 2 2x^4 + 2(2x)^2 + 8x^2 + (x+1) + (x+1)^2 - 2 16x^4 + 8x^3 + 9x^2 + 2x -1 Is that what you drew?

21. triciaal

you did not copy exactly what I had but I think you got the general idea

22. triciaal

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23. anonymous

Original: f(x) = 4x^2 + x + 1; g(x) = x^2 – 2 Combine: (4x^2 + x + 1)^2 - 2 Factor: (4x^2 + x + 1) (4x^2 + x + 1) - 2 Expand: 16x^4 + 4x^3 + 9x^2 + 4x^3 + x^2 + x + 1 - 2 Solve: 16x^4 + 8x^3 + 9x^2 + 2x -1

24. triciaal

not factor expand not expand simplify yes