Question

Factor 360t + 10t ^3 - 120t ^2.

10t(t - 6)(t + 6)
10t(t - 6)^2
-10t(t - 6)(t + 6)

Answer 1

The answer is: [B]: " 10t (t - 6)² "
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Note:
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Choice [A]: 10t(t - 6)(t + 6) = 10t (t² - 36) = 10t³ - 360t .

Choice [C]: is similar; except with "-10t" in lieu of "10t" :
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-10t (t-6)(t+6) = -10t (t² -36) = -10t³ + 360t ;
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This leaves us with the remaining answer choice:
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Answer choice: [B]: " 10t (t - 6)² " .
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But let us check:

(t - 6)² = (t - 6)(t - 6) = t² - 6t - 6t + 36 = t² - 12t + 36 ;

10t (t² - 12t + 36) = 10t³ - 120t² + 360t ;

which equals the value presented in the question:
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which is: 360t + 10t³ - 120t² "

Note: "our solved value: " 10t³ - 120t² + 360t " = ?
(the value in the question: " 360t + 10t³ - 120t² " ?

360t + 10t³ - 120t² =? 10t³ - 120t² + 360t ??

= +360t +10t³ - 120t² ?? YES!
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The answer is: [B]: " 10t (t - 6)² " .
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