Factor the trinomial

Question

4c²+21c+5

Answer 1

Ashley, let me show you one way to do this.

 

First, we have to multiply 4 x 5  (the first and last numbers) to get 20.

 

Now, we want two factors of 20 that add together to make 21, the middle number.

 

1 x 20, 2 x 10, 4 x 5.  Which of those pairs add together to make 21? 1 + 20 = 21, right?

 

So, we are going to split up 21c into 1c + 20c and plug that into our trinomial

 

4c² + 1c + 20c + 5

 

Now the kinda tricky part.  What is common between the first two terms?  c, right? We can factor it out.

 

4c² + 1c = c(4c + 1)

 

Now, what is common between the last two terms? 5, right? We can factor it out.

 

20c + 5 = 5(4c + 1)

 

Notice how we have the same thing in both sets of parentheses!  Since we are multiplying two things by the same thing, like 1x + 20x = 21x, we can add the two things together.  We can't combine c and 5, though, so they stay separate in their own parentheses.

 

c(4c+1) + 5(4c+1) = (c+5)(4c+1)

 

I hope this helps!

Answer 2

Use FOIL Method:

 

Factors of 4 are 4(1), 2(2), -4(-1), -2(-2)

Factors of 5 are 5(1), -5(-1)

 

(4c+1)(c+5)