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Author Jonathan David Author of Fiction
Author Jonathan David
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Factoring 5x² + x − 8 Using the Quadratic Formula | Sample from The Ultimate Crash Course Series

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      Sample from The Ultimate Crash Course Series

      Get the full bundle with structured lessons and over 1,000 lessons and podcasts via 
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      theSTEMmajor.com.
    

  






Factor 5x² + x − 8




General Quadratic Form




5x^2+x-8=ax^2+bx+c




Quadratic Formula




x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}







Check if Factorable




b^2-4ac=1^2-4(5)(-8)=1+160=161>0





Since the discriminant is positive but not a perfect square, the polynomial has two irrational roots. Therefore, it is not factorable using integer coefficients.




Find the Roots




x=\frac{-1\pm\sqrt{161}}{2(5)}





x=\frac{-1\pm\sqrt{161}}{10}




Write in Factored Form




x=-\frac{1+\sqrt{161}}{10},\quad x=-\frac{1-\sqrt{161}}{10}





\left(x+\frac{1+\sqrt{161}}{10}\right)\left(x+\frac{1-\sqrt{161}}{10}\right)=0




Final Factored Form




\boxed{\left(x+\frac{1+\sqrt{161}}{10}\right)\left(x+\frac{1-\sqrt{161}}{10}\right)}







Algebra Insight




Not all quadratics factor nicely using integers. When the discriminant is not a perfect square, the quadratic formula provides the exact factorization using irrational roots.






  

    
    

      Sample from The Ultimate Crash Course Series

      This lesson is part of the Ultimate Crash Course bundle. Get the full collection at 
      Payhip 
      and access over 1,000 lessons and podcasts through 
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