Question

More Challenges:

Answer 1

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