Question #5f8be

3 Answers
Sep 15, 2017

#(5x-4)(3x+1)#

Explanation:

I remember receiving this problem before . . . Here's how my math teacher explained it:

You can't factor this the way you normally would with quadratic equations, becuase there are no two numbers whose sum is 7 and whose product is 4.

So, you just have to experiment with the problem by inputting factors of #-4# into

#(x-a)(x+b)#

The answer is:

#(5x-4)(3x+1)#

If you FOIL the expression, you'll end up with the original equation.

Sep 15, 2017

#x# = #4/5# and - #1/3#

Explanation:

In short, bring over the 4 and factor by grouping
You always have to make the equation equal to zero when factoring so in this case you would bring the 4 over.
#15x^2##-##7x##-#4

NOTE: you can get rid of the zero, it doesn't matter now

Then factor by grouping,
- Multiply the last number by the leading coefficient, in this case 15.
15 * -4 = -60

  • Don't replace the - 4 with -60 just find two numbers that add up to -7, but multiplies to -60
  • In this case it would be -12 and 5
  • Now replace the -#7x# with -#12# and #5#

#15x^2##+##5x#-12x#-#4

NOTE: I placed them the way they are so that when we factor it, it will give us whole numbers

  • Then factor by splitting the equation in half
  • Factor #15x^2##+##5x# and #-12x##-#4 individually
  • Add brackets to separate them

#5x#(#3x##+#1) #-# 4 (3#x# + 1)

Now since the numbers are the same you can write it as one, then combine what's outside of the bracket together

(#5x##-#4)(#3x##+#1)

NOTE: You know you did right if the numbers in the brackets are the same

NORMALLY, you would be done, however the #x#'s need to be by itself, so you would solve for #x# within each bracket by making it equal to zero

#5x##-#4 = 0
#5x# = 4
#x# = #4/5#

#3x##+#1 = 0
#3x# = - 1
#x# = -#1/3#

Therefore, #x# = #4/5# and - #1/3#

Sep 15, 2017

#- 1/3 and 4/5#

Explanation:

To avoid doing the lengthy factoring by grouping, you may use the new Transforming Method (Socratic, Google Search)
#y = 15x^2 - 7x - 4 = 0#
Converted equation:
#y' = x^2 - 7x - 60#.
Proceeding: Find 2 real roots of y', then, divide them by a = 15
The 2 real roots of y' are: - 5 and 12 -->
[Sum = 7 = - b] and Product {ac = - 60]
The 2 real roots of y are: #x1 = - 5/15 = -1/3# and #x2 = 12/15 = 4/5#.