How do you factor the expression #5x^2 - 16x + 3#?

1 Answer
Dec 4, 2015

Answer:

#(5x-1)(x-3)#

Explanation:

Given: #5x^2-16x+3#

The 3 is a prime number so can only have {1, 3} as factors.
It is positive so the signs in the brackets are the same
The coefficient of x is negative (-16x) so they must both be negative.

The 5 is also a prime number so can only have {1, 5} as factors.

It is just a matter of getting them in the correct order

#color(blue)("Attempt 1")#

#(5x-3)(x-1) = 5x^2-8x ...color(red)("Fail")#

This will not work so there is no point in continuing with the rest of the multiplication.

#color(blue)("Attempt 2")#

#color(blue)((5x-1)(x-3))color(brown)(=5x^2-15x-x+3)color(blue)(=5x^2-16x+3)#