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14. Factor x4 + 3x2 - 28.(x2 - 7)(x - 2)(x + 2)(x2 - 2)(x2 + 14)(x2 + 7)(x - 2)(x + 2)(x2 + 4)(x2 - 7)

14. Factor x4 + 3x2 - 28.(x2 - 7)(x - 2)(x + 2)(x2 - 2)(x2 + 14)(x2 + 7)(x - 2)(x-example-1
User Callmeed
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Answer:


x^4+3x^2-28=(x^2+7)(x-2)(x+2)

Explanation:

To factorize the expression, we can use a variable substitution. Let's say that z=x^2.


\begin{gathered} x^4+3x^2-28 \\ z^2+3z-28 \end{gathered}

Then, to factorize this we need to factor in the form:


(z+\text{?)(z}+\text{?)}

The numbers that go in the blanks, have to:

*Add together to get 3


-4+7=3

*Multiply together to get -28


-4\cdot7=-28

So, we get:


z^2+3z-28=(z-4)(z+7)

Substitute the equation z=x^2


(x^2-4)(x^2+7)

Factorizing the perfect square binomial:


x^4+3x^2-28=(x^2+7)(x-2)(x+2)

User Vagoberto
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