Which of the following is a factor of the expression 24x^2-30x-9? Group of answer choices

12x+1

4x-3

2x+3

4x+1

4x + 1

Step-by-step explanation:

24x² - 30x - 9 ( factor out 3 from each term )

= 3(8x² - 10x - 3) ← factor the quadratic

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 8 × - 3 = - 24 and sum = - 10

the factors are + 2 and - 12

use these factors to split the x- term

8x² + 2x - 12x - 3 ( factor the first/second and third/fourth terms )

= 2x(4x + 1) - 3(4x + 1) ← factor out (4x + 1) from each term

= (4x + 1)(2x - 3)

then

24x² - 30x - 9 = 3(4x + 1)(2x - 3) ← in factored form

so (4x + 1) is a factor of the expression

true !

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!