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

If 4x + 5 is a factor of 12x^2 - x + c, what is the value of C ?-example-1
User Moscas
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1 Answer

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23 votes

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

User Knut Forkalsrud
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