Question

Question #5f8be

Answer 1

`(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.

Answer 2

`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`

Answer 3

`- 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`.