Question

If 4x + 5 is a factor of 12x^2 - x + c, what is the value of C ?

Answer 1

If 4x+5 is a factor of 12x^2-x+c, this means that

`12x^2-x+c=(ax+b)(4x+5)=4ax^2+4bx+5ax+5b=4ax^2+(4b+5a)x+5b`

Where a and b are two constants.

Then, we can find the values of a and b as follows:

`\begin{gathered} 12x^2=4ax^2 \\ \Rightarrow a=3 \\ -x=(4b+5a)x \\ \Rightarrow-1=(4b+5a)=4b+5\cdot3=4b+15 \\ \Rightarrow-16=4b \\ \Rightarrow b=-4 \end{gathered}`

Finally, we can find the value of c

`\begin{gathered} c=5b \\ \Rightarrow c=5(-4)=-20 \\ \Rightarrow c=-20 \end{gathered}`

The answer is c=-20