Answer:
1. [tex]-m(-8n^2-7n+1)[/tex]
2. [tex](2w+7c) (v+7c)[/tex]
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:
- [tex]8mn^2+7mn-m\\-m(-8n^2-7n+1)[/tex]
Notice the term [tex](-8n^2-7n+1)[/tex] 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.
[tex](2vw + 7cv) + (14cw + 49c^2)\\v(2w+7c)+7c(2w+7c)[/tex]
Notice that (2w+7c) is the same. The factoring is complete. The factors are:
[tex](2w+7c) (v+7c)[/tex]
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
[tex]a^3 + b^3 = (a + b)(a^2 -ab + b^2)[/tex].
To use this form, take the cube root of each term. a = q and b=3r.
The factors are [tex](q+3)(q^2-3qr+9r^2)[/tex]
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
