Show all work to factor x^4 − 5x^2 + 4 completely.

Step-by-step explanation:

We want to factor the expression .

First, notice that this is in quadratic form. In other words, both the exponents have even power.

Therefore, we can make a substitution to simplify the expression.

So, let’s let .

Our expression is the same as:

Substitute:

Now, we can factor like normal. We can use -1 and -4. Therefore:

We can now substitute back u:

Both of these can be factored furthered using the difference of two squares:

Therefore, we will have:

And we are done!

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

happy to

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