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FinnZ [79.3K]
3 years ago
13

Factor completely 3x^2+7x-6

Mathematics
2 answers:
Likurg_2 [28]3 years ago
7 0
I find the following method easiest to factor this equation.

1. First, fill in what you know would be the factors for the first value, 3x^2.  The number 3 only has 2 factors: 3 and 1. Therefore, we know the first values are:

(3x _____)(x_____)

2. Next, figure out what the possible factors for the last value would be (-6). The following combinations are possible:
2 and -3 OR -3 and 2
-2 and 3 OR 3 and -2
-1 and 6  OR 6 and -1
1 and -6 OR -6 and 1

3. Plug in the combinations into step 1 and see which gives you the correct answer:
<span>(3x + 2)(x - 3) = 3x^2 - 7x - 6 --> no
</span>(3x - 3)(x + 2<span>) = 3x^2 + 3x - 6 --> no
</span>(3x - 2)(x + 3) = 3x^2 + <span>7x - 6 --> YES</span>
vaieri [72.5K]3 years ago
6 0
Factor \ 3x^2+7x-6 

1. \ Multiply \ 3 \ by \ -6, \ which \ is \ -18.

2. \ Ask: \ Which \ two \ numbers \ add  \ up \ to \ 7 \ and  \ multiply \ to -18?

Answer: \ 9  \ and \ -2

4. \ Rewrite \ 7x \ as \ the \ sum \ of \ 9x \ and  \ -2x:

&#10;3x^2+9x-2x-6&#10; &#10;&#10; 
 
&#10;3x(x+3)-2(x+3)&#10; &#10;  Factor \ out \ common \ terms \ in \ the \ first \ two \ terms,  then \ in \ the \ last two \ terms 

(x+3)(3x-2) Factor \ out \ the \ common \ term  \ x+3

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phil ate three less than twice as many pancakes as sara. together they combined to eat 15 pancakes. How many pancakes did each e
Levart [38]

Answer:

Let x represents the Sara eat pancake and y represents the Phil eat the pancake.

As per the statement:

Phil ate three less than twice as many pancakes as Sara.

"Twice as many pancake as Sara" means 2x

"three less than twice as many pancakes as Sara" means 2x -3

⇒y = 2x-3         .....[1]

It is also given that together they combined to eat 15 pancakes.

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Add 3 to both sides we get;

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A househusband is cooking beef stew for his family in a pan that is (a) uncovered, (b) covered with a light lid, and (c) covered
raketka [301]

Answer:

Cooking will be shortest when the househusband covers the beef stew with the heavy lid.

Step-by-step explanation:

The explanation for this is that water boils at 100°C at normal atmospheric pressure & it remains at that temperature until all the water evaporates as steam; the temperature can then go higher in steam form.

So, if he leaves the pan uncovered the pressure above the beef stew will be the atmospheric pressure and the temperature of the stew will not pass the 100°C mark and the food cooks at 100°C.

If he places a light lid on top, the pressure will build up & the temperature at which water remains liquid is a bit higher, but eventually the steam will push the lid to escape thereby releasing pressure & reducing the temperature.

If he puts a heavy lid on the pan the pressure can build up the highest and the temperature of the water in the stew will stay the highest ensuring the fastest cooking.

Basically, the heavier the lid, greater the pressure in the pan. As the pressure gets greater, the saturation temperature at which water starts boiling will be higher. And higher boiling temperatures mean shorter cooking times.

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