More challenges: 1) factor out the indicated quantity.8mn² + 7mn - m : factor out the quantity -m2) factor the polynomial by grouping.2vw + 7cv + 14cw + 49c²3) factor completely using the difference of squares along with factoring by grouping.25v³ - 25v² - 4v + 44) factor the sum of cubes. 125x³ + 645) q³ + 27r³6) factor completely. use difference of squares.729p^6 - 6^67) solve the equation(7x + 4)(9x - 1) = 08) a. find the values of x for which f (x) = 0b. find f (0)f (x) = x² + 2x - 489) find the x and y-intercepts for the function defined by y = f (x)f (x) = (x + 3)(x + 4)(x - 1)²10) factor the trinomial completely by using any method. remember to look for a common factor first. 3v² - 2v - 16

1.

2.

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:

Notice the term 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.

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

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

.

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

The factors are

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

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9

there are infinitely many solutions.