Question

Which statement about 4x2 + 19x – 5 is true? One of the factors is (x – 4). One of the factors is (4x + 1). One of the factors is (4x – 5). One of the factors is (x + 5).

Answer 1

`4 x^(2) + 19x - 5 \\ \\ 4 x^(2) + 20x - x - 5 \\ \\ 4x(x + 5)-(x + 5) \\ \\ (x + 5)(4x - 1)`

The answer is D) one of the factors of (x + 5). Why?

(x - 4) is not one of the factors.
(4x + 1) is not one of the factors.
(4x - 5) is not one of the factors.
(x + 5) IS one of the factors.

Answer 2

Only "One of the factors is (x + 5)." is TRUE.

Explanation:

• What makes
  `(x-4)` equal to 0?

`x-4=0\\x=4`

• What makes
  `(4x+1)` equal to 0?

`4x+1=0\\4x=-1\\x=-(1)/(4)`

• What makes
  `(4x-5)` equal to 0?

`4x-5=0\\4x=5\\x=(5)/(4)`

• What makes
  `(x+5)` equal to 0?

`x+5=0\\x=-5`

Note: Putting all those 4 values into the function
`4x^(2)+19x-5`, whichever value makes the function equal to 0, the corresponding expression would be considered a factor of the function
`4x^2+19x-5`.

• Putting
  `x=4` into
  `4x^(2)+19x-5` gives us:

`4(4)^(2)+19(4)-5\\=135`

• Putting
  `x=-(1)/(4)` into
  `4x^(2)+19x-5` gives us:

`4(-(1)/(4))^(2)+19(-(1)/(4))-5\\=-(19)/(2)`

• Putting
  `x=(5)/(4)` into
  `4x^(2)+19x-5` gives us:

`4((5)/(4))^(2)+19((5)/(4))-5\\=25`

• Putting
  `x=-5` into
  `4x^(2)+19x-5` gives us:

`4(-5)^(2)+19(-5)-5\\=0`

As we can see, only putting
`x=-5` in the function gives us a value of 0. So the corresponding expression
`(x+5)` is a factor of the function.