Questions
Solve for x by factoring.
\(\textbf{1)}\) \( x^2+10x-24=0 \)
The answer is \( x=-12,2 \)
\(\,\,\,\,\,x^2+10x-24=0\)
\(\,\,\,\,\,(x+12)(x-2)=0\)
\(\,\,\,\,\,x+12=0 \text{ or }x-2=0\)
\(\,\,\,\,\,x=-12 \text{ or }x=2\)
\(\textbf{2)}\) \( 2x^2+7x=4 \)
The answer is \( x= -4, \frac{1}{2} \)
\(\,\,\,\,\,2x^2+7x=4\)
\(\,\,\,\,\,2x^2+7x-4=0\)
\(\,\,\,\,\,(2x-1)(x+4)=0\)
\(\,\,\,\,\,2x-1=0 \text{ or }x+4=0\)
\(\,\,\,\,\,x=\frac{1}{2} \text{ or }x=-4\)
\(\textbf{3)}\) \( x^2-6x+8=0 \)
The answer is \( x=2,4 \)
\(\,\,\,\,\,x^2-6x+8=0\)
\(\,\,\,\,\,(x-2)(x-4)=0\)
\(\,\,\,\,\,x-2=0 \text{ or }x-4=0\)
\(\,\,\,\,\,x=2 \text{ or }x=4\)
\(\textbf{4)}\) \( x^2-4=0\)
The answer is \(x=\pm2\)
\(\,\,\,\,\,x^2-4=0=0\)
\(\,\,\,\,\,(x+2)(x-2)=0\)
\(\,\,\,\,\,x+2=0 \text{ or }x-2=0\)
\(\,\,\,\,\,x=-2 \text{ or }x=2\)
\(\textbf{5)}\) \( x^2-4x+4=0\)
The answer is \(x=2\)
\(\,\,\,\,\,x^2-4x+4=0=0\)
\(\,\,\,\,\,(x-2)(x-2)=0\)
\(\,\,\,\,\,x-2=0\)
\(\,\,\,\,\,x=2\)
\(\textbf{6)}\) \( x^2-5x+4=0\)
The answer is \(x=1,4\)
\(\,\,\,\,\,x^2-5x+4=0\)
\(\,\,\,\,\,(x-1)(x-4)=0\)
\(\,\,\,\,\,x-1=0 \text{ or }x-4=0\)
\(\,\,\,\,\,x=1 \text{ or }x=4\)
\(\textbf{7)}\) \( x^2+3x+2=0\)
The answer is \(x=-2,-1\)
\(\,\,\,\,\,x^2+3x+2=0\)
\(\,\,\,\,\,(x+1)(x+2)=0\)
\(\,\,\,\,\,x+1=0 \text{ or }x+2=0\)
\(\,\,\,\,\,x=-1 \text{ or }x=2\)
\(\textbf{8)}\) Write a quadratic equation with solutions \(3\) and \(-4\).
The answer is \( x^2+x-12=0 \)
\(\,\,\,\,\,x=3 \text{ or }x=-4\)
\(\,\,\,\,\,x-3=0 \text{ or }x+4=0\)
\(\,\,\,\,\,(x-3)(x+4)=0\)
\(\,\,\,\,\,x^2+x-12=0\)
\(\textbf{9)}\) Write a quadratic equation with solutions \(\frac{1}{2}\) and \(5\).
The answer is \( 2x^2-11x+5=0 \)
\(\,\,\,\,\,x=\frac{1}{2} \text{ or }x=5\)
\(\,\,\,\,\,x-\frac{1}{2}=0 \text{ or }x-5=0\)
\(\,\,\,\,\,2x-1=0 \text{ or }x-5=0\)
\(\,\,\,\,\,(2x-1)(x-5)=0\)
\(\,\,\,\,\,2x^2-11x+5=0\)
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