Question

More Challenges:

1) Factor out the indicated quantity.
8mn² + 7mn - m : Factor out the quantity -m

2) Factor the polynomial by grouping.
2vw + 7cv + 14cw + 49c²

3) Factor completely using the difference of squares along with factoring by grouping.
25v³ - 25v² - 4v + 4

4) Factor the sum of cubes.
125x³ + 64

5) q³ + 27r³

6) Factor completely. Use difference of squares.
729p^6 - 6^6

7) Solve the equation
(7x + 4)(9x - 1) = 0

8)
a. Find the values of x for which f (x) = 0
b. Find f (0)
f (x) = x² + 2x - 48

9) Find the x and y-intercepts for the function defined by y = f (x)
f (x) = (x + 3)(x + 4)(x - 1)²

10) Factor the trinomial completely by using any method. Remember to look for a common factor first. 3v² - 2v - 16

Answer 1

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.

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