MHB Need help factoring and understanding Grouping

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    Factoring Grouping
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To factor the expression 6t^2 + 17t + 7, first break it down into 6t^2 + 3t + 14t + 7. Next, group the terms: factor out 3t from the first group (6t^2 + 3t) and 7 from the second group (14t + 7). This results in 3t(2t + 1) + 7(2t + 1), revealing a common factor of (2t + 1). Finally, factor out the common term to obtain the fully factored form: (2t + 1)(3t + 7). Understanding these steps is crucial for mastering polynomial factoring techniques.
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I need to factor 6t^2+17t+7 when I break down the equation I get 6t^2+3t+14t+7 now I am not sure what to do after that to get my answer can someone please explain the steps for me thank you!
 
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hououin kyouma said:
I need to factor 6t^2+17t+7 when I break down the equation I get 6t^2+3t+14t+7 now I am not sure what to do after that to get my answer can someone please explain the steps for me thank you!

Factorise the first two terms, and factorise the second two terms. Then you should see a common factor.
 
hououin kyouma said:
I need to factor 6t^2+17t+7 when I break down the equation I get 6t^2+3t+14t+7
I presume you wrote it that way because you can now factor "3t" out of "6t^2+ 3t and factor "7" out of "14t+ 7". What does that leave?

now I am not sure what to do after that to get my answer can someone please explain the steps for me thank you!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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