Question

~~~~~~~~~FAN AND MEDAL!~~~~~~~~~~~~~~
Determine whether the following polynomials can be factored by grouping. If so, factor the polynomials showing all work. If not, explain why this method will not work.

2c2 + 6cd + 5c + 15d
3a2 + 6ab + 4a + 4b

Answer 1

a. 2c2 + 6cd + 5c + 15d
Group:
(2c^2 + 6cd) + (5c + 15d)
Factor out the common factor:
2c (c + 3d) + 5 (c + 3d)
Use the distributive property:
(c + 3d) (2c + 5)

b. 3a2 + 6ab + 4a + 4b
The ratio of 3:6 is different than the ratio 4:4 so this can't be factored by grouping. In fact it can't be factored in real numbers.

In order to create a polynomial that can be factored, start by choosing the factors. For example:
(2a + 3b) (5c - 7d)
Multiply the chosen factors together:
10ac - 14ad + 15bc - 21bd
In order to factor that polynomial, being by grouping:
(10ac - 14ad) + (15bc - 21bd)
Factor out the common factors:
2a (5c - 7d) + 3b (5c - 7d)
Use the distributive property:
(5c - 7d) (2a + 3b)

Answer 2

Do you understand ?

Answer 3

okay just reading over it

Answer 4

Oh i see now yes this makes sense thank u so much

Answer 5

By your Friendly Neighborhood Spider-Man