MHB Yes, that is correct! Great job factoring the expression.

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The expression t^4 - 9t^2 + 20 is factored by substituting u = t^2, transforming it into u^2 - 9u + 20. This factors to (u - 5)(u - 4), which is then back-substituted to yield (t^2 - 5)(t^2 - 4). The term t^2 - 4 is identified as the difference of two perfect squares, leading to the final factorization of (t^2 - 5)(t - 2)(t + 2). The solution is confirmed as correct, with a note about more factoring questions to come.
mathdad
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Factor the expression.

t^4 - 9t^2 + 20

My Solution

(t^2)^2 - 9t^2 + 20

Let u = t^2

u^2 - 9u + 20

(u - 5)(u - 4)

I can back-substitute for u.

(t^2 - 5)(t^2 - 4)

I see that t^2 - 4 is the difference of two perfect squares.

Answer: (t^2 - 5)(t - 2)(t + 2)

Correct?
 
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Looks good. (Yes)
 
MarkFL said:
Looks good. (Yes)

Very good. Good night. More factoring questions on Friday.
 

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