Factor x^2-2x-3

Problem

x2−2⁢x−3 x squared minus 2 x minus 3

Solution

  1. Identify the coefficients of the quadratic expression in the form a⁢x2+b⁢x+c a x squared plus b x plus c where a=1 a equals 1 b=−2 b equals negative 2 and c=−3 c equals negative 3

  2. Find two numbers that multiply to c c (which is −3 negative 3 and add to b b (which is −2 negative 2.

  3. Determine the factors by testing pairs: the numbers −3 negative 3 and 1 1 satisfy both conditions because (−3)⁢(1)=−3 negative 3 times 1 equals negative 3 and −3+1=−2 negative 3 plus 1 equals negative 2

  4. Write the expression in factored form (x+p)⁢(x+q) open paren x plus p close paren times open paren x plus q close paren using the numbers found.

Final Answer

x2−2⁢x−3=(x−3)⁢(x+1) x squared minus 2 x minus 3 equals open paren x minus 3 close paren times open paren x plus 1 close paren

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