factorise 3x^2-17x-28 (can you show me the working out)

Question

anonymous · Answer

please reply as I am stuck with my homework

campbell_st · Answer

ok... this is how I do it.... it's not something you see in textbooks... but it does work... 

for a quadratic 

$$ax^2 + bx + c $$

multiply a and c 

so in your question, you multiply 

3 and -28   = -84

find the factor that add to -17 with the larger factor negative 

factors of -84 = 4 and -21   

then you write it as 

(ax + factor 1)(ax + fractor 2)
-------------------------
                       a

so you have 

$$\frac{(3x -21)(3x + 4)}{3}$$

factor the binomials in the numerator and you get

$$\frac{3(x - 7)(3x + 4)}{3}$$

now you can cancel the common factor for the solution. 

works every time for a difficult to factor quadratic. 

hope it helps