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gizmo_the_mogwai [7]
3 years ago
11

More Challenges:

Mathematics
1 answer:
kenny6666 [7]3 years ago
3 0

Answer:

1. -m(-8n^2-7n+1)

2. (2w+7c) (v+7c)

5. (q+3r)(q^2-3qr+9r^2)

7. x= - 4/7,  1/9

See below for additional problems and help.

Step-by-step explanation:

To factor polynomials, look for patterns and greatest common factors. When you remove these factors, write the factor and what remains.

For example:

  1. 8mn^2+7mn-m\\-m(-8n^2-7n+1)

Notice the term (-8n^2-7n+1) is left and is the term when the expression is divided by -m.

     2. Factor by grouping is similar. Pull out factors within pairs of term. Separate the terms by parenthesis. If the quantities in the [parenthesis are the same, the factoring has been successful.

(2vw + 7cv) + (14cw + 49c^2)\\v(2w+7c)+7c(2w+7c)

Notice that (2w+7c) is the same. The factoring is complete. The factors are:

(2w+7c) (v+7c)

3 - 6 is similar using specific forms for factoring. To find the forms, look in your notes or at resources on online. Here is one example.

      4. A sum of cubes has the form

a^3 + b^3 = (a + b)(a^2 -ab + b^2).

To use this form, take the cube root of each term. a = q and b=3r.

The factors are (q+3)(q^2-3qr+9r^2)

7-9 all involve factoring and then solving. You solve by setting the factors equal to 0.

7. (7x+4)(9x-1) = 0

(7x+4) = 0                      (9x-1)=0

7x=-4                               9x = 1

x= - 4/7                             x = 1/9

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In base 5 the place values (from right to left) are the ones place, the 5's place and the 25's place.  The highest digit you can write in any column is a 4.   

333 would be (3 x 25) + (3 x 5) + (3 x 1) which is 93 in base 10.
30 would be (3x5) + (0 x 1)  which is 15 in base 10.
The sum of 93 and 15 is 108 in base 10.
Now lets write that in base 5 -    We can have 4 25's so there will be a 4 in the 25's column.  Since 4 x 25 = 100 we still have to account for 8 to get to 108.
We can have 1 five  in the 5's columns since 1 x 5 is 5.  Now we have 3 left over which we can place in the one's column
Final answer 333₅ + 30₅ = 413₅
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