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xxMikexx [17]
3 years ago
7

Factor 5x 4 - 30x 2 - 135.

Mathematics
2 answers:
Alex787 [66]3 years ago
5 0
5x^4 - 30x^2 - 135 \\ \\ GCF = 5 \\ \\ 5( \frac{5x^4}{5} +  \frac{-30x^2}{5} -  \frac{135}{5} ) \\ \\ 5(x^2 - 6x^2 - 27) \\ \\ 5(x^2 - 9)(x^2 + 3) \\ \\ 5(x^2 - 3^2)(x^2 + 3) \\ \\ 5(x + 3)(x - 3)(x^2 + 3) \\ \\

The final result is: 5(x + 3)(x - 3)(x<span>² +3).</span>
GenaCL600 [577]3 years ago
4 0
5x⁴ -30x² - 135

Factorizing 5x⁴ -30x² - 135,   Factoring out 5

5( x⁴ -6x² - 27)..............................(a)

Factoring ( x⁴ -6x² - 27). 

x⁴ -6x² - 27 = (x²)² -6(x²) - 27

Let y = x²

Therefore  (x²)² -6(x²) - 27 = y² -6y - 27

Therefore (a)  is the same as:  

5( x⁴ -6x² - 27) = 5(y² -6y - 27)...........(b)

y² -6y - 27 is a quadratic expression

Multiplying first and last terms = y² * -27 = -27y²

We think of two factors that multiply up to -27y², and add up to -6y which is the middle term of the quadratic expression.

The factors are :     -9y and +3y

Check:  (-9y)*(+3y) = -27y²,    +3y + (-9y) = 3y -9y = -6y 

In the expression y² -6y - 27, we replace the middle term -6y with (3y - 9y)

y² -6y - 27

y² +3y - 9y- 27

y(y+3) - 9(y+3)

(y+3)(y-9)

 y² -6y - 27 =  (y+3)(y-9) ........................(c)    

Recall y = x²

(y+3)(y-9) = (x²+3)(x²-9) ........................(d)

But (x²-9) is difference of two squares = x² - 3² = (x-3)(x+3)

(x²+3)(x²-9)

(x²+3)(x-3)(x+3) ...........................(e)

Therefore from (b)

5(x⁴ -6x² - 27) = 5(y² -6y - 27)

5(y² -6y - 27) = 5(y+3)(y-9)  =  5(x²+3)(x²-9) = 5(x²+3)(x-3)(x+3)

So 5x⁴ -30x² - 135  is =  5(x²+3)(x-3)(x+3)

I hope this helps.
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18 + 14 + (56+63)/72

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33 and 47/72


3 0
3 years ago
Read 2 more answers
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I don't understand how to do this. :'(
natulia [17]

Answer:

Step-by-step explanation:

First and foremost, all quadratics have a domain of all real numbers (as long as we are not given only a portion of the graph, or one with endpoints. Our graph does not have endpoints, so it is assumed that the tails will continue to go down into negative infinity and at the same time, the x coordinates will keep growing as well.) Since our quadratic is upside down, it has a max. That means that none of the values on the graph will be above that point. All the values will be below that highest point (the highest y-value). Y-values indicate range, and since our highest y-value is at y = 2, then the range is

y ≤ 2

3 0
3 years ago
Help is greatly appreciated!
Masja [62]

Answer:

∛3, ∛3 to the fourth power, 3³∕ ², 3³∕ ², radical 3 to the fifth power

Step-by-step explanation:

I'm going to convert all these to decimal form to make it easier.

3³∕ ² = 4.5

∛3 = 1.44

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3 years ago
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Question 2 2.1 2.2 2.2.1 2.2.2 Determine the general solution for sin(x - 30°) = cos 2x Consider the functions f(x) = sin(x-30°)
OLEGan [10]

The general solution for the given equation is 40°+120°n.

The period of g(x) is π.

The range of f(x) is [-1, 1].

  • sin(x-30°) = cos 2x
  • sin(x-30°) = sin(90°-2x)
  • (x-30°) = (90°-2x) + 360°n
  • x + 2x =  90° + 30° + 360°n
  • 3x = 120° + 360°n
  • x = (120° + 360°n)/3
  • The general solution (x) is 40° + 120°n.
  • g(x) = cos 2x
  • The period of cos x is 2π.
  • If the multiplying factor of x is 'n', then it decreases the period by n times.
  • Here, in g(x), n is 2.
  • The period of g(x) is equal to half the period of cos x.
  • The period of g(x) = 2π/2
  • The period of g(x) is π.
  • f(x) = sin(x-30°)
  • "Sin" is a trigonometric function which has a range from -1 to 1.

To learn more about  period, visit :

brainly.com/question/12539110

#SPJ9

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