Show all work to factor x^4-10x^2+9 completely

Quadratic equations are also a type of algebraic fractions that have factors.

The factor of

In order to completely factor we would apply the formula:

a(x-r)(x-s)

To find the variables a, x, r and s, we have to love at the coefficients of which is -10 and the term 9 and find out what can we multiply together to give us 9 and add together to give us -10

That would be , -9 and - 1 because:

-9 x -1 = 9

-9 + (-1) = -10

Hence: the value for a = 1

, r = -9  and s = -1

Putting this into the equation:

1(x -(-9)(x - (-1))

Hence, we have:

Factorizing the above expression further, we have

Therefore, the factor of

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Step-by-step explanation:

Step 1: Find what adds to _ and multiples to_

It needs to multiple to the 'c' term or 9

It needs to add to the 'b' term or -10

Step 2: Find the numbers

We know -9 and -1 make 10 and multiple to 9

-9 x -1 = 9

-9 + (-1) + -10

Step 3: Write equation in form a(x-r)(x-s)

a = 1

r = -9

s = -1

Plug in the equation to get the factored form of the equation:

Therefore the factored form of the equation is

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step-by-step explanation: