Factor 2x^2-13x+20

Problem

2⁢x2−13⁢x+20 2 x squared minus 13 x plus 20

Solution

  1. Identify the coefficients of the quadratic expression a⁢x2+b⁢x+c a x squared plus b x plus c where a=2 a equals 2 b=−13 b equals negative 13 and c=20 c equals 20

  2. Calculate the product a⁢c a c which is 2×20=40 2 times 20 equals 40

  3. Find two numbers that multiply to 40 40 and add to the middle coefficient b=−13 b equals negative 13 These numbers are −8 negative 8 and −5 negative 5

  4. Rewrite the middle term −13⁢x negative 13 x using the two numbers found: −8⁢x−5⁢x negative 8 x minus 5 x

2⁢x2−8⁢x−5⁢x+20 2 x squared minus 8 x minus 5 x plus 20

  1. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

2⁢x⁢(x−4)−5⁢(x−4) 2 x times open paren x minus 4 close paren minus 5 times open paren x minus 4 close paren

  1. Factor out the common binomial (x−4) open paren x minus 4 close paren

(2⁢x−5)⁢(x−4) open paren 2 x minus 5 close paren times open paren x minus 4 close paren

Final Answer

2⁢x2−13⁢x+20=(2⁢x−5)⁢(x−4) 2 x squared minus 13 x plus 20 equals open paren 2 x minus 5 close paren times open paren x minus 4 close paren

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