# How do you factor completely 45t^4 - 90t^3 + 25t^2?

Apr 18, 2016

Just to clarify what the other contributor was saying...

#### Explanation:

Factor out the GCF.

$5 {t}^{2} \left(9 {t}^{2} - 18 t + 5\right)$

The expression inside the parentheses can be factored as a trinomial of the form $y = a {x}^{2} + b x + c , a \ne 1$. To do this, we must find two numbers that multiply to $a \times c$ and that add to b, and then follow the following process. Two numbers that do this are -15 and -3.

$5 {t}^{2} \left(9 {t}^{2} - 3 t - 15 t + 5\right)$

$5 {t}^{2} \left(3 t \left(3 t - 1\right) - 5 \left(3 t - 1\right)\right)$

$5 {t}^{2} \left(3 t - 5\right) \left(3 t - 1\right)$

This is completely factored.

Hopefully this helps!
The text passage contains a mathematical question about factoring a polynomial expression and provides a detailed step-by-step answer to the question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# How do you factor completely 45t^4 - 90t^3 + 25t^2?

Apr 18, 2016

Just to clarify what the other contributor was saying...

#### Explanation:

Factor out the GCF.

$5 {t}^{2} \left(9 {t}^{2} - 18 t + 5\right)$

The expression inside the parentheses can be factored as a trinomial of the form $y = a {x}^{2} + b x + c , a \ne 1$. To do this, we must find two numbers that multiply to $a \times c$ and that add to b, and then follow the following process. Two numbers that do this are -15 and -3.

$5 {t}^{2} \left(9 {t}^{2} - 3 t - 15 t + 5\right)$

$5 {t}^{2} \left(3 t \left(3 t - 1\right) - 5 \left(3 t - 1\right)\right)$

$5 {t}^{2} \left(3 t - 5\right) \left(3 t - 1\right)$

This is completely factored.

Hopefully this helps!
user
The text passage contains a mathematical question about factoring a polynomial expression and provides a detailed step-by-step answer to the question.

TYPE: SINGLE_QUESTION_WITH_ANSWER