Question

Factor: 5x2 + 4x - 1

Answer 1

You should try this one on your own.

Answer 2

I'll tell you that it looks like
(5x + something)(x + something)

Find the somethings that work

Answer 3

(5x + 4)(x - 1)?

Answer 4

Multiple that out and you'll see you get
\[ 5x^2 -x -4 \] so that's not quite right.

Answer 5

If
\[ 5x^2+4x−1= (5x+a)(x+b) \]

then notice that
\[ (5x+a)(x+b)=5x2+(a+5b)x+ab \]

Hence it must be that
\[ ab=−1 \]

and
\[ a+5b=4 \]


Find a and b such those two statements are true.

Answer 6

5x^2+4x-1


5x^2+5x-x-1 ... Note: 5 and -1 add to 4 (the middle coefficient) and multiply to -5 (the product of the first and last coefficients)


(5x^2+5x)+(-x-1)


5x(x+1)+(-x-1)


5x(x+1)-1(x+1)


(5x-1)(x+1)



So 5x^2+4x-1 completely factors to (5x-1)(x+1)