Factor. 4x^2 + 5x + 1

Question

Having some trouble. Could someone help out. I get stuck on the second step.

Answer 1

Factoring is tricky and it can also be hard to explain but I'll try.

 

We have to find the factors of the first number and the third number so that when we multiply those factors then add the result, we get the middle number.

 

So the factors of the first number (4) are: 4*1 and 2*2.  The factors of the third number (1) are 1*1.  So now we have to find the right combination of those factors that add up to the middle number (5).

 

If we look at 2*1 + 2*1, we get 2 + 2, or 4, which does not equal 5.

 

If we look at 4*1 + 1*1, we get 4+1, which equals 5.

 

So the factored form of 4x² + 5x + 1 is (4x + 1)(x + 1)