Question

If someone could help explain how to do 17-19 that would be great I really am lost and if someone could give me a step by step but at this point any help is good

Answer 1

Answer:

17: see below.

18: x = 2; x = -2; x = 3i;  x = - 3i

19:  x = sqrt(3); x= - sqrt(3); x = 1 ; x = - 1

Step-by-step explanation:

17

Short answer No without doing anything. The 61 must be factorable using 6 as a factor. 61 is prime. But that's not really what you want to know although it is the answer. You look like you are doing synthetic division, so we'll answer it that way.

6 || 1    - 7     - 3      61

             6     -6      -54  

====================

     1      -1      -9        7

The answer is x^2 - x  - 9 with remainder of 7 / (x - 6)

18

x^4 + 5x^2 - 36 = 0

Substitute z for x^2

z^2 + 5z - 36 = 0   This factors.

(z + 9) (z - 4) = 0     Put the x^2 into the factors.

x^2 - 4 = 0              Add 4 to both sides  

x^2 = 4                   Take the square root of both sides.

x = +/- 2

===============

x^2 + 9 = 0

x^2 = - 9                      Take the square root of both sides

sqrt(x^2) = sqrt(-9)      

x = +/- 3i

19

19 is done exactly as 18 was done. You should get 4 real roots.

The graph is below. Very briefly it is going to factor as

(x^2 - 3)(x^2 - 1)

The results are x = sqrt(3); x= - sqrt(3); x = 1 ; x = - 1