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Factor f(a) = 7a²– 16a + 4

User Aurand
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1 Answer

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Factor this expression means to find two numbers x and y such that we can write f(a) = (a+x)(a+y).

To do this, we use the quadratic formula


\begin{gathered} a=\frac{-(-16)\pm\sqrt[]{(-16)^2-4(7)(4)}}{2(7)} \\ a=\frac{16\pm\sqrt[]{256-112}}{14} \\ a=\frac{16\pm\sqrt[]{144}}{14} \\ a=(16\pm12)/(14) \end{gathered}

so, one answer is


a=(16+12)/(14)=(28)/(14)=2

and the other one


a=(16-12)/(14)=(4)/(14)=(2)/(7)

To find the factors we use the solutions


\begin{gathered} a=2\text{ then a-2=0} \\ a-2\text{ is a factor} \end{gathered}
\begin{gathered} a=(2)/(7)\text{ then 7a-2=0} \\ 7a-2\text{ is a factor} \end{gathered}

Then, the factorization is


7a^2-16a+4=(7a-2)(a-2)

User Donald Wu
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