How to factor

Question

I need help with this question

 

20w^2+11w-3

Answer 1

Hi! To factor the quadratic, we first write it: y = 20w^2 + 11w - 3 and identify the three coefficients as: 20 = a 11 = b -3 = c We then write the product ac, and look for factors of ac that add up to b. 20(-3) = -60 The factors -4 and 15 add up to 11. Now, we just pick leading coefficients that give us a total of 11w when we foil the factors. Since -3 is a prime number, we use -1 and 3 for the constant terms in the linear factors. (3) times 5 is 15, and -1 times 4 is -4, so we write: (4w + 3)(5w - 1) = 20w^2 (First) - 4w (Outer) + 15w (Inner) -3 (Last) to give us the original quadratic. Best, Joe

Answer 2

Another approach is to use factoring by grouping.  

 

First, multiply the coefficient of w² by the constant term: (20)(-3) = -60

 

Find two integers whose product is -60 and whose sum is the coefficient of w, 11.

 

We see that 15 and -4 are two such integers

 

Rewrite 11x as 15x-4x and factor by grouping:

 

20w² + 11w - 3 = 20w² + 15w - 4w - 3

 

                      = 5w(4w+3) -1(4w+3)

 

                      = (4w+3)(5w-1)